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On the automorphisms of the classical groups. With a supplement by Loo-Keng Hua
About this Title
Jean Dieudonné
Publication: Memoirs of the American Mathematical Society
Publication Year:
1951; Number 2
ISBNs: 978-0-8218-1202-0 (print); 978-0-8218-9961-8 (online)
DOI: https://doi.org/10.1090/memo/0002
MathSciNet review: 0045125
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