Isomorphisms of symplectic groups over commutative rings (Q795173)
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scientific article; zbMATH DE number 3861437
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Isomorphisms of symplectic groups over commutative rings |
scientific article; zbMATH DE number 3861437 |
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Isomorphisms of symplectic groups over commutative rings (English)
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1983
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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)].
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epimorphisms of symplectic groups
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standard automorphisms
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