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Hardcover ISBN:  9780821805169 
Product Code:  DIMACS/28 
List Price:  $114.00 
MAA Member Price:  $102.60 
AMS Member Price:  $91.20 
eBook ISBN:  9781470439866 
Product Code:  DIMACS/28.E 
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MAA Member Price:  $96.30 
AMS Member Price:  $85.60 
Hardcover ISBN:  9780821805169 
eBook ISBN:  9781470439866 
Product Code:  DIMACS/28.B 
List Price:  $221.00 $167.50 
MAA Member Price:  $198.90 $150.75 
AMS Member Price:  $176.80 $134.00 

Book DetailsDIMACS  Series in Discrete Mathematics and Theoretical Computer ScienceVolume: 28; 1997; 382 ppMSC: Primary 20
The workshop “Groups and Computations” took place at the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) at Rutgers University in June 1995. This and an earlier workshop (see Groups and Computation, Finkelstein and Kantor, ©1993, American Mathematical Society) held in October 1991 was aimed at merging theory and practice within the broad area of computation with groups. The primary goal of the previous workshop was to foster a dialogue between researchers studying the computational complexity of group algorithms and those engaged in the development of practical software. It was expected that this would lead to a deeper understanding of the mathematical issues underlying group computation and that this understanding would lead, in turn, to faster algorithms. Comments and subsequent work indicated that this goal had been achieved beyond expectations. The second workshop was designed to reinforce the progress in these directions.
The scientific program consisted of invited lectures and research announcements, as well as informal discussions and software demonstrations. The eight extended talks discussed randomization, permutation groups, matrix groups, software systems, fast Fourier transforms and their applications to signal processing and data analysis, computations with finitely presented groups, and implementation and complexity questions. As in the previous workshop, speakers ranged from established researchers to graduate students.
Copublished with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1–7 were copublished with the Association for Computer Machinery (ACM).
ReadershipGraduate students and research mathematicians interested in computational methods.

Table of Contents

Chapters

Randomization in group algorithms: Conceptual questions

Experimenting and computing with infinite groups

Towards polynomial time algorithms for matrix groups

Calculating the order of an invertible matrix

A nonconstructive recognition algorithm for the special linear and other classical groups

GAP/MPI: Facilitating parallelism

Constructive recognition of a black box group isomorphic to $GL(n,2)$

Special presentations for finite soluble groups and computing (pre)Frattini subgroups

Algorithms for group actions applied to graph generation

Partitions, refinements, and permutation group computation

A polycyclic quotient algorithm

Computing the fitting subgroup and solvable radical of smallbase permutation groups in nearly linear time

Generalized FFTs–A survey of some recent results

The complexity of McKay’s canonical labeling algorithm

On nearly linear time algorithms for Sylow subgroups of smallbase permutation groups

Implementing a recognition algorithm for classical groups

Algorithms for polycyclicbyfinite matrix groups

Asymptotic results for simple groups and some applications

Some applications of generalized FFTs

Constructing permutation representations for matrix groups in parallel environments


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The workshop “Groups and Computations” took place at the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) at Rutgers University in June 1995. This and an earlier workshop (see Groups and Computation, Finkelstein and Kantor, ©1993, American Mathematical Society) held in October 1991 was aimed at merging theory and practice within the broad area of computation with groups. The primary goal of the previous workshop was to foster a dialogue between researchers studying the computational complexity of group algorithms and those engaged in the development of practical software. It was expected that this would lead to a deeper understanding of the mathematical issues underlying group computation and that this understanding would lead, in turn, to faster algorithms. Comments and subsequent work indicated that this goal had been achieved beyond expectations. The second workshop was designed to reinforce the progress in these directions.
The scientific program consisted of invited lectures and research announcements, as well as informal discussions and software demonstrations. The eight extended talks discussed randomization, permutation groups, matrix groups, software systems, fast Fourier transforms and their applications to signal processing and data analysis, computations with finitely presented groups, and implementation and complexity questions. As in the previous workshop, speakers ranged from established researchers to graduate students.
Copublished with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1–7 were copublished with the Association for Computer Machinery (ACM).
Graduate students and research mathematicians interested in computational methods.

Chapters

Randomization in group algorithms: Conceptual questions

Experimenting and computing with infinite groups

Towards polynomial time algorithms for matrix groups

Calculating the order of an invertible matrix

A nonconstructive recognition algorithm for the special linear and other classical groups

GAP/MPI: Facilitating parallelism

Constructive recognition of a black box group isomorphic to $GL(n,2)$

Special presentations for finite soluble groups and computing (pre)Frattini subgroups

Algorithms for group actions applied to graph generation

Partitions, refinements, and permutation group computation

A polycyclic quotient algorithm

Computing the fitting subgroup and solvable radical of smallbase permutation groups in nearly linear time

Generalized FFTs–A survey of some recent results

The complexity of McKay’s canonical labeling algorithm

On nearly linear time algorithms for Sylow subgroups of smallbase permutation groups

Implementing a recognition algorithm for classical groups

Algorithms for polycyclicbyfinite matrix groups

Asymptotic results for simple groups and some applications

Some applications of generalized FFTs

Constructing permutation representations for matrix groups in parallel environments