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The Santa Cruz Conference on Finite Groups
Edited by:
Bruce Cooperstein
Hardcover ISBN:  9780821814406 
Product Code:  PSPUM/37 
List Price:  $139.00 
MAA Member Price:  $125.10 
AMS Member Price:  $111.20 
eBook ISBN:  9780821893265 
Product Code:  PSPUM/37.E 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
Hardcover ISBN:  9780821814406 
eBook: ISBN:  9780821893265 
Product Code:  PSPUM/37.B 
List Price:  $274.00 $206.50 
MAA Member Price:  $246.60 $185.85 
AMS Member Price:  $219.20 $165.20 
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The Santa Cruz Conference on Finite Groups
Edited by:
Bruce Cooperstein
Hardcover ISBN:  9780821814406 
Product Code:  PSPUM/37 
List Price:  $139.00 
MAA Member Price:  $125.10 
AMS Member Price:  $111.20 
eBook ISBN:  9780821893265 
Product Code:  PSPUM/37.E 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
Hardcover ISBN:  9780821814406 
eBook ISBN:  9780821893265 
Product Code:  PSPUM/37.B 
List Price:  $274.00 $206.50 
MAA Member Price:  $246.60 $185.85 
AMS Member Price:  $219.20 $165.20 

Book DetailsProceedings of Symposia in Pure MathematicsVolume: 37; 1981; 634 ppMSC: Primary 20

Table of Contents

Part I: Classification theory of simple finite groups

Daniel Gorenstein — An outline of the classification of finite simple groups [ MR 604552 ]

Michael Aschbacher — Groups of characteristic $2$type [ MR 604553 ]

Richard Foote — Aschbacher blocks [ MR 604554 ]

Ronald Solomon — Some results on standard blocks [ MR 604555 ]

Richard Lyons — Signalizer functors in groups of characteristic $2$ type [ MR 604556 ]

John H. Walter — The $B$conjecture: $2$components in finite simple groups [ MR 604557 ]

Ronald Solomon — The maximal $2$component approach to the $B(G)$ conjecture [ MR 604558 ]

Morton E. Harris — Finite groups having an involution centralizer with a $2$component of dihedral type [ MR 604559 ]

Morton E. Harris — On Chevalley groups over fields of odd order, the unbalanced group conjecture and the $B(G)$conjecture [ MR 604560 ]

Kensaku Gomi — Remarks on certain standard component problems and the unbalanced group conjecture [ MR 604561 ]

Robert Gilman — Odd standard components [ MR 604562 ]

Izumi Miyamoto — Standard subgroups of Chevalley type of rank $2$ and characteristic $2$ [ MR 604563 ]

Hiromichi Yamada — Standard subgroups of type $G_{2}(3)$ [ MR 604564 ]

Larry Finkelstein — Open standard form problems [ MR 604565 ]

F. Timmesfeld — Groups generated by a conjugacy class of involutions [ MR 604566 ]

Stephen D. Smith — The classification of finite groups with large extraspecial $2$subgroups [ MR 604567 ]

Sergei Syskin, A. — Some characterization theorems [ MR 604568 ]

Bernd Stellmacher — On finite groups whose Sylow $2$subgroups are contained in unique maximal subgroups [ MR 604569 ]

G. Stroth — Groups having a selfcentralizing elementary abelian subgroup of order $16$ [ MR 604570 ]

George Glauberman — $p$local subgroups [ MR 604571 ]

George Glauberman — Local analysis in the odd order paper

Michio Suzuki — Finite groups with a split $BN$pair of rank one [ MR 604572 ]

Koichiro Harada — Finite groups of low $2$rank, revisited [ MR 604573 ]

Geoffrey Mason — Quasithin groups [ MR 604574 ]

Part II: General theory of groups

Helmut Wielandt — Zusammengesetzte Gruppen: Hölders Programm heute [ MR 604575 ]

Walter Feit — Some consequences of the classification of finite simple groups [ MR 604576 ]

John McKay — Graphs, singularities, and finite groups [ MR 604577 ]

Hsio Fu Tuan — Works on finite group theory by some Chinese mathematicians [ MR 604578 ]

J. S. Williams — The prime graph components of finite groups [ MR 604579 ]

Zvi Arad and David Chillag — $\pi $solvability and nilpotent Hall subgroups [ MR 604580 ]

Zvi Arad, Marcel Herzog and Ahiezer Shaki — On maximal subgroups with a nilpotent subgroup of index $2$ [ MR 604581 ]

Anthony Hughes — Automorphisms of nilpotent groups and supersolvable orders [ MR 604582 ]

A. R. Camina — A short survey of Fitting classes [ MR 604583 ]

Tomoyuki Yoshida — Transfer theorems [ MR 604584 ]

Gilbert Baumslag — Problem areas in infinite group theory for finite group theorists [ MR 604585 ]

L. G. Kovács — Classification theorems for torsionfree groups [ MR 604586 ]

Part III: Properties of the known groups

Gary M. Seitz — Properties of the known simple groups [ MR 604587 ]

Gary M. Seitz — The root groups of a maximal torus [ MR 604588 ]

B. Cooperstein — Geometry of long root subgroups in groups of Lie type [ MR 604589 ]

B. Cooperstein — $S$ and $F$pairs for groups of Lie type in characteristic two [ MR 604590 ]

T. A. Springer — Geometric questions arising in the study of unipotent elements [ MR 604591 ]

Robert Steinberg — Kleinian singularities and unipotent elements [ MR 604592 ]

Simon Norton — The construction of $J_{4}$ [ MR 604593 ]

Robert L. Griess, Jr. — Schur multipliers of the known finite simple groups. II [ MR 604594 ]

M. A. Ronan and S. D. Smith — $2$local geometries for some sporadic groups [ MR 604595 ]

Part IV: Representation theory of groups of Lietype

Charles W. Curtis — Problems concerning characters of finite groups of Lie type [ MR 604596 ]

R. W. Carter — The relation between characteristic $0$ representations and characteristic $p$ representations of finite groups of Lie type [ MR 604597 ]

George Lusztig — Some problems in the representation theory of finite Chevalley groups [ MR 604598 ]

Leonard L. Scott — Representations in characteristic $p$ [ MR 604599 ]

Bhama Srinivasan — Characters of finite groups of Lie type. II [ MR 604600 ]

R. W. Kilmoyer — Principal series representations of finite groups with split $(BN)$pairs [ MR 604601 ]

J. E. Humphreys — Cartan invariants and decomposition numbers of Chevalley groups [ MR 604602 ]

Dean Alvis — Duality in the character ring of a finite Chevalley group [ MR 604603 ]

Leonard Chastkofsky — Characters of projective indecomposable modules for finite Chevalley groups [ MR 604604 ]

N. B. Tinberg — Some indecomposable modules of groups with split $(B,\,N)$pairs [ MR 604605 ]

Part V: Character theory of finite groups

J. L. Alperin — Local representation theory [ MR 604606 ]

I. M. Isaacs — Characters of solvable groups [ MR 604607 ]

Lluís Puig — Local block theory in $p$solvable groups [ MR 604608 ]

Dilip Gajendragadkar — Characters of finite $\pi $separable groups [ MR 604609 ]

Michel Broué — On characters of height zero [ MR 604610 ]

Harvey I. Blau — Brauer trees and character degrees [ MR 604611 ]

Everett C. Dade — A correspondence of characters [ MR 604612 ]

Walter Feit — Irreducible modules of $p$solvable groups [ MR 604613 ]

Pamela A. Ferguson — Finite complex linear groups of degree less than $(2q+1)/3$ [ MR 604614 ]

Peter Landrock and Gerhard O. Michler — A criterion for cyclicity [ MR 604615 ]

David Gluck — A characterization of generalized permutation characters [ MR 604616 ]

Marcel Herzog — Character tables, trivial intersections and number of involutions [ MR 604617 ]

T. R. Berger — Representation theory and solvable groups: length type problems [ MR 604618 ]

Part VI: Combinatorics

Marshall Hall, Jr. — Group problems arising from combinatorics [ MR 604619 ]

Ernest Shult — Grouprelated geometries [ MR 604620 ]

Saeed Shad and Ernest Shult — Near $n$gons [ MR 604621 ]

Eiichi Bannai — Orthogonal polynomials, algebraic combinatorics and spherical $t$designs [ MR 604622 ]

T. G. Ostrom — Finite translation planes and group representation [ MR 604623 ]

Christoph Hering — Finite collineation groups of projective planes containing nontrivial perspectivities [ MR 604624 ]

William M. Kantor — Further problems concerning finite geometries and finite groups [ MR 604625 ]

Part VII: Computer applications

John J. Cannon — Effective procedures for the recognition of primitive groups [ MR 604626 ]

John J. Cannon — Software tools for group theory [ MR 604627 ]

Volkmar Felsch — The computation of a counterexample to the classbreadth conjecture for $p$groups [ MR 604628 ]

David C. Hunt — A computerbased atlas of finite simple groups [ MR 604629 ]

Jeffrey S. Leon — Finding the order of a permutation group [ MR 604630 ]

Part VIII: Connections with number theory and other fields

A. P. Ogg — Modular functions [ MR 604631 ]

J. G. Thompson — A finiteness theorem for subgroups of $\mathrm {PSL}(2,\,\mathbf {R})$ which are commensurable with $\mathrm {PSL}(2,\,\mathbf {Z})$ [ MR 604632 ]

Paul Fong — Characters arising in the Monstermodular connection [ MR 604633 ]

Larissa Queen — Modular functions and finite simple groups [ MR 604634 ]

J. Lepowsky — Euclidean Lie algebras and the modular function $j$ [ MR 604635 ]

M. Fried — Exposition on an arithmeticgroup theoretic connection via Riemann’s existence theorem [ MR 604636 ]

D. Husemoller — Burnside ring of a Galois group and the relations between zeta functions of intermediate fields [ MR 604637 ]

D. Husemoller — Finite automorphism groups of algebraic varieties [ MR 604638 ]

Ted Petrie — Transformation groups and representation theory [ MR 604639 ]

I. M. Isaacs — Lie algebras with nilpotent centralizers [ MR 604640 ]


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 Table of Contents
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Part I: Classification theory of simple finite groups

Daniel Gorenstein — An outline of the classification of finite simple groups [ MR 604552 ]

Michael Aschbacher — Groups of characteristic $2$type [ MR 604553 ]

Richard Foote — Aschbacher blocks [ MR 604554 ]

Ronald Solomon — Some results on standard blocks [ MR 604555 ]

Richard Lyons — Signalizer functors in groups of characteristic $2$ type [ MR 604556 ]

John H. Walter — The $B$conjecture: $2$components in finite simple groups [ MR 604557 ]

Ronald Solomon — The maximal $2$component approach to the $B(G)$ conjecture [ MR 604558 ]

Morton E. Harris — Finite groups having an involution centralizer with a $2$component of dihedral type [ MR 604559 ]

Morton E. Harris — On Chevalley groups over fields of odd order, the unbalanced group conjecture and the $B(G)$conjecture [ MR 604560 ]

Kensaku Gomi — Remarks on certain standard component problems and the unbalanced group conjecture [ MR 604561 ]

Robert Gilman — Odd standard components [ MR 604562 ]

Izumi Miyamoto — Standard subgroups of Chevalley type of rank $2$ and characteristic $2$ [ MR 604563 ]

Hiromichi Yamada — Standard subgroups of type $G_{2}(3)$ [ MR 604564 ]

Larry Finkelstein — Open standard form problems [ MR 604565 ]

F. Timmesfeld — Groups generated by a conjugacy class of involutions [ MR 604566 ]

Stephen D. Smith — The classification of finite groups with large extraspecial $2$subgroups [ MR 604567 ]

Sergei Syskin, A. — Some characterization theorems [ MR 604568 ]

Bernd Stellmacher — On finite groups whose Sylow $2$subgroups are contained in unique maximal subgroups [ MR 604569 ]

G. Stroth — Groups having a selfcentralizing elementary abelian subgroup of order $16$ [ MR 604570 ]

George Glauberman — $p$local subgroups [ MR 604571 ]

George Glauberman — Local analysis in the odd order paper

Michio Suzuki — Finite groups with a split $BN$pair of rank one [ MR 604572 ]

Koichiro Harada — Finite groups of low $2$rank, revisited [ MR 604573 ]

Geoffrey Mason — Quasithin groups [ MR 604574 ]

Part II: General theory of groups

Helmut Wielandt — Zusammengesetzte Gruppen: Hölders Programm heute [ MR 604575 ]

Walter Feit — Some consequences of the classification of finite simple groups [ MR 604576 ]

John McKay — Graphs, singularities, and finite groups [ MR 604577 ]

Hsio Fu Tuan — Works on finite group theory by some Chinese mathematicians [ MR 604578 ]

J. S. Williams — The prime graph components of finite groups [ MR 604579 ]

Zvi Arad and David Chillag — $\pi $solvability and nilpotent Hall subgroups [ MR 604580 ]

Zvi Arad, Marcel Herzog and Ahiezer Shaki — On maximal subgroups with a nilpotent subgroup of index $2$ [ MR 604581 ]

Anthony Hughes — Automorphisms of nilpotent groups and supersolvable orders [ MR 604582 ]

A. R. Camina — A short survey of Fitting classes [ MR 604583 ]

Tomoyuki Yoshida — Transfer theorems [ MR 604584 ]

Gilbert Baumslag — Problem areas in infinite group theory for finite group theorists [ MR 604585 ]

L. G. Kovács — Classification theorems for torsionfree groups [ MR 604586 ]

Part III: Properties of the known groups

Gary M. Seitz — Properties of the known simple groups [ MR 604587 ]

Gary M. Seitz — The root groups of a maximal torus [ MR 604588 ]

B. Cooperstein — Geometry of long root subgroups in groups of Lie type [ MR 604589 ]

B. Cooperstein — $S$ and $F$pairs for groups of Lie type in characteristic two [ MR 604590 ]

T. A. Springer — Geometric questions arising in the study of unipotent elements [ MR 604591 ]

Robert Steinberg — Kleinian singularities and unipotent elements [ MR 604592 ]

Simon Norton — The construction of $J_{4}$ [ MR 604593 ]

Robert L. Griess, Jr. — Schur multipliers of the known finite simple groups. II [ MR 604594 ]

M. A. Ronan and S. D. Smith — $2$local geometries for some sporadic groups [ MR 604595 ]

Part IV: Representation theory of groups of Lietype

Charles W. Curtis — Problems concerning characters of finite groups of Lie type [ MR 604596 ]

R. W. Carter — The relation between characteristic $0$ representations and characteristic $p$ representations of finite groups of Lie type [ MR 604597 ]

George Lusztig — Some problems in the representation theory of finite Chevalley groups [ MR 604598 ]

Leonard L. Scott — Representations in characteristic $p$ [ MR 604599 ]

Bhama Srinivasan — Characters of finite groups of Lie type. II [ MR 604600 ]

R. W. Kilmoyer — Principal series representations of finite groups with split $(BN)$pairs [ MR 604601 ]

J. E. Humphreys — Cartan invariants and decomposition numbers of Chevalley groups [ MR 604602 ]

Dean Alvis — Duality in the character ring of a finite Chevalley group [ MR 604603 ]

Leonard Chastkofsky — Characters of projective indecomposable modules for finite Chevalley groups [ MR 604604 ]

N. B. Tinberg — Some indecomposable modules of groups with split $(B,\,N)$pairs [ MR 604605 ]

Part V: Character theory of finite groups

J. L. Alperin — Local representation theory [ MR 604606 ]

I. M. Isaacs — Characters of solvable groups [ MR 604607 ]

Lluís Puig — Local block theory in $p$solvable groups [ MR 604608 ]

Dilip Gajendragadkar — Characters of finite $\pi $separable groups [ MR 604609 ]

Michel Broué — On characters of height zero [ MR 604610 ]

Harvey I. Blau — Brauer trees and character degrees [ MR 604611 ]

Everett C. Dade — A correspondence of characters [ MR 604612 ]

Walter Feit — Irreducible modules of $p$solvable groups [ MR 604613 ]

Pamela A. Ferguson — Finite complex linear groups of degree less than $(2q+1)/3$ [ MR 604614 ]

Peter Landrock and Gerhard O. Michler — A criterion for cyclicity [ MR 604615 ]

David Gluck — A characterization of generalized permutation characters [ MR 604616 ]

Marcel Herzog — Character tables, trivial intersections and number of involutions [ MR 604617 ]

T. R. Berger — Representation theory and solvable groups: length type problems [ MR 604618 ]

Part VI: Combinatorics

Marshall Hall, Jr. — Group problems arising from combinatorics [ MR 604619 ]

Ernest Shult — Grouprelated geometries [ MR 604620 ]

Saeed Shad and Ernest Shult — Near $n$gons [ MR 604621 ]

Eiichi Bannai — Orthogonal polynomials, algebraic combinatorics and spherical $t$designs [ MR 604622 ]

T. G. Ostrom — Finite translation planes and group representation [ MR 604623 ]

Christoph Hering — Finite collineation groups of projective planes containing nontrivial perspectivities [ MR 604624 ]

William M. Kantor — Further problems concerning finite geometries and finite groups [ MR 604625 ]

Part VII: Computer applications

John J. Cannon — Effective procedures for the recognition of primitive groups [ MR 604626 ]

John J. Cannon — Software tools for group theory [ MR 604627 ]

Volkmar Felsch — The computation of a counterexample to the classbreadth conjecture for $p$groups [ MR 604628 ]

David C. Hunt — A computerbased atlas of finite simple groups [ MR 604629 ]

Jeffrey S. Leon — Finding the order of a permutation group [ MR 604630 ]

Part VIII: Connections with number theory and other fields

A. P. Ogg — Modular functions [ MR 604631 ]

J. G. Thompson — A finiteness theorem for subgroups of $\mathrm {PSL}(2,\,\mathbf {R})$ which are commensurable with $\mathrm {PSL}(2,\,\mathbf {Z})$ [ MR 604632 ]

Paul Fong — Characters arising in the Monstermodular connection [ MR 604633 ]

Larissa Queen — Modular functions and finite simple groups [ MR 604634 ]

J. Lepowsky — Euclidean Lie algebras and the modular function $j$ [ MR 604635 ]

M. Fried — Exposition on an arithmeticgroup theoretic connection via Riemann’s existence theorem [ MR 604636 ]

D. Husemoller — Burnside ring of a Galois group and the relations between zeta functions of intermediate fields [ MR 604637 ]

D. Husemoller — Finite automorphism groups of algebraic varieties [ MR 604638 ]

Ted Petrie — Transformation groups and representation theory [ MR 604639 ]

I. M. Isaacs — Lie algebras with nilpotent centralizers [ MR 604640 ]
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