Isomorphisms of symplectic groups over commutative rings. (English. Russian original) Zbl 0542.20029
Algebra Logic 22, 397-405 (1983); translation from Algebra Logika 22, No. 5, 551-562 (1983).
The isomorphisms of symplectic groups over arbitrary commutative rings are described. Let R, \(R_ 1\) be commutative rings. It is proved in particular, that every isomorphism between the groups G and \(G_ 1\) where \(ESp_{2n}(R)\leq G\leq Sp_{2n}(R),\quad ESp_{2m}(R_ 1)\leq G_ 1\leq Sp_{2m}(R_ 1),\quad n,m\geq 3\) is standard; it gives an affirmative answer to the question 8.46 by Yu. I. Merzlyakov from The Kourovka Notebook [8th ed. (1982; Zbl 0509.20001)].
MSC:
| 20G35 | Linear algebraic groups over adèles and other rings and schemes |
| 20E36 | Automorphisms of infinite groups |
Citations:
Zbl 0509.20001References:
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