Includes bibliographical references.

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 Dieudonn�e on the automorphisms of classical groups I. Linear groups II. Orthogonal groups

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

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