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On the Automorphisms of the Classical Groups
 
J. Dieudonné
On the Automorphisms of the Classical Groups
eBook ISBN:  978-0-8218-9961-8
Product Code:  MEMO/1/2.E
List Price: $23.00
MAA Member Price: $20.70
AMS Member Price: $18.40
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On the Automorphisms of the Classical Groups
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On the Automorphisms of the Classical Groups
J. Dieudonné
eBook ISBN:  978-0-8218-9961-8
Product Code:  MEMO/1/2.E
List Price: $23.00
MAA Member Price: $20.70
AMS Member Price: $18.40
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1; 1951; 123 pp
    MSC: Primary 20
  • Table of Contents
     
     
    • Chapters
    • I. Introduction
    • II. Automorphisms of $\textrm {GL}_n(K)$ ($n \geq 3$, $K$ sfield of characteristic $\neq 2$)
    • III. Automorphisms of $\textrm {PGL}_n(K)$ ($n \geq 3$, $K$ sfield of characteristic $\neq 2$)
    • IV. Automorphisms of $\textrm {GL}_n(K)$ and $\textrm {PGL}_n(K)$ ($n \geq 3$, $K$ sfield of characteristic 2)
    • V. Automorphisms of $\textrm {SL}_n(K)$ and $\textrm {PSL}_n(K)$
    • VI. Automorphisms of $\textrm {Sp}_{2m}(K)$ ($K$ field of characteristic $\neq 2$)
    • VII. Automorphisms of $\textrm {PSp}_n(K)$ ($K$ field of characteristic $\neq 2$)
    • VIII. Automorphisms of $\textrm {Sp}_{2m}(K)$ ($K$ field of characteristic 2)
    • IX. Isomorphisms between the groups $\textrm {PSp}_{2m}(K)$ and the groups $\textrm {PSL}_n(K’)$ and $\mathfrak {A}_r$
    • X. Automorphisms of ${\mathrm {O}}_n(K,f)$ ($n \geq 3$, $K$ field of characteristic $\neq 2$, $f$ quadratic form of index $\nu \geq 1$)
    • XI. Automorphisms of ${\mathrm {O}}^+_n(K,f)$ ($n \geq 5$, $K$ field of characteristic $\neq 2$, $f$ quadratic form of index $\nu \geq 1$)
    • XII. Automorphisms of $\textrm {PO}_n(K,f)$ and $\textrm {PO}^+_n(K,f)$ ($n$ even $\geq 4$, $K$ field of characteristic $\neq 2$, $f$ quadratic form of index $\nu \geq 1$)
    • XIII. Automorphisms of ${\mathrm {P}}\Omega _n(K,f)$ ($n \geq 6$, $K$ finite field of characteristic $\neq 2$)
    • XIV. Automorphisms of ${\mathrm {P}}\Omega _n(K,f)$ ($n$ even $\geq 10$, $K$ finite field of characteristic 2)
    • XV. Isomorphisms between the groups ${\mathrm {P}}\Omega _n(K,f)$ and $\textrm {PSL}_n(K’)$, $\textrm {PSp}_k(K’)$ or $\mathfrak {A}_r$ ($K$ finite field)
    • XVI. Automorphisms of $\mathrm {U}_n(K,f)$ ($n \geq 3$, $K$ field of characteristic $\neq 2$, $f$ hermitian form of index $\nu \geq 1$)
    • XVII. Automorphisms of $U^+_n(K,f)$ ($n \geq 3$, $K$ field of characteriatic $\neq 2$, $f$ hermitian form of index $\nu \geq 1$)
    • XVIII. Automorphisms of the group $\mathrm {U}_n(K,f)$ ($n \geq 3$, $K$ reflexive sfield of characteristic $\neq 2$, $f$ hermitian form of index $\nu \geq 1$)
    • XIX. Automorphisms of $\textrm {PU}^+_n(K)$ ($n \geq 3$, $K$ finite field of characteristic $\neq 2$)
    • XX. Automorphisms of $\textrm {PU}^+_n(K)$ ($n \geq 3$, $K$ finite field of characteristic 2)
    • XXI. Isomorphisms between the groups $\textrm {PU}^+_n(K)$ and $\textrm {PSL}_n(K’)$, $\textrm {PSp}_k(K’)$, $\mathrm {P}\Omega _m(K’,f’)$ or $\mathfrak {A}_r$ ($K$ finite field)
    • XXII. Conclusion
    • Supplement to the paper of Dieudonné on the automorphisms of classical groups
    • I. Linear groups
    • II. Orthogonal groups
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Memoirs of the American Mathematical Society
Volume: 1; 1951; 123 pp
MSC: Primary 20
  • Chapters
  • I. Introduction
  • II. Automorphisms of $\textrm {GL}_n(K)$ ($n \geq 3$, $K$ sfield of characteristic $\neq 2$)
  • III. Automorphisms of $\textrm {PGL}_n(K)$ ($n \geq 3$, $K$ sfield of characteristic $\neq 2$)
  • IV. Automorphisms of $\textrm {GL}_n(K)$ and $\textrm {PGL}_n(K)$ ($n \geq 3$, $K$ sfield of characteristic 2)
  • V. Automorphisms of $\textrm {SL}_n(K)$ and $\textrm {PSL}_n(K)$
  • VI. Automorphisms of $\textrm {Sp}_{2m}(K)$ ($K$ field of characteristic $\neq 2$)
  • VII. Automorphisms of $\textrm {PSp}_n(K)$ ($K$ field of characteristic $\neq 2$)
  • VIII. Automorphisms of $\textrm {Sp}_{2m}(K)$ ($K$ field of characteristic 2)
  • IX. Isomorphisms between the groups $\textrm {PSp}_{2m}(K)$ and the groups $\textrm {PSL}_n(K’)$ and $\mathfrak {A}_r$
  • X. Automorphisms of ${\mathrm {O}}_n(K,f)$ ($n \geq 3$, $K$ field of characteristic $\neq 2$, $f$ quadratic form of index $\nu \geq 1$)
  • XI. Automorphisms of ${\mathrm {O}}^+_n(K,f)$ ($n \geq 5$, $K$ field of characteristic $\neq 2$, $f$ quadratic form of index $\nu \geq 1$)
  • XII. Automorphisms of $\textrm {PO}_n(K,f)$ and $\textrm {PO}^+_n(K,f)$ ($n$ even $\geq 4$, $K$ field of characteristic $\neq 2$, $f$ quadratic form of index $\nu \geq 1$)
  • XIII. Automorphisms of ${\mathrm {P}}\Omega _n(K,f)$ ($n \geq 6$, $K$ finite field of characteristic $\neq 2$)
  • XIV. Automorphisms of ${\mathrm {P}}\Omega _n(K,f)$ ($n$ even $\geq 10$, $K$ finite field of characteristic 2)
  • XV. Isomorphisms between the groups ${\mathrm {P}}\Omega _n(K,f)$ and $\textrm {PSL}_n(K’)$, $\textrm {PSp}_k(K’)$ or $\mathfrak {A}_r$ ($K$ finite field)
  • XVI. Automorphisms of $\mathrm {U}_n(K,f)$ ($n \geq 3$, $K$ field of characteristic $\neq 2$, $f$ hermitian form of index $\nu \geq 1$)
  • XVII. Automorphisms of $U^+_n(K,f)$ ($n \geq 3$, $K$ field of characteriatic $\neq 2$, $f$ hermitian form of index $\nu \geq 1$)
  • XVIII. Automorphisms of the group $\mathrm {U}_n(K,f)$ ($n \geq 3$, $K$ reflexive sfield of characteristic $\neq 2$, $f$ hermitian form of index $\nu \geq 1$)
  • XIX. Automorphisms of $\textrm {PU}^+_n(K)$ ($n \geq 3$, $K$ finite field of characteristic $\neq 2$)
  • XX. Automorphisms of $\textrm {PU}^+_n(K)$ ($n \geq 3$, $K$ finite field of characteristic 2)
  • XXI. Isomorphisms between the groups $\textrm {PU}^+_n(K)$ and $\textrm {PSL}_n(K’)$, $\textrm {PSp}_k(K’)$, $\mathrm {P}\Omega _m(K’,f’)$ or $\mathfrak {A}_r$ ($K$ finite field)
  • XXII. Conclusion
  • Supplement to the paper of Dieudonné on the automorphisms of classical groups
  • I. Linear groups
  • II. Orthogonal groups
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