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Isomorphisms Between Linear Groups Over Division Rings

Published online by Cambridge University Press:  20 November 2018

Vasilij M. Petechuk
Vasilij M. Petechuk*
Affiliation:
5, Sechenov St. Uzhgorod, Transcarpathia Ukraine
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Abstract

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In the present paper we completely describe the isomorphisms between projective elementary groups PSLn and PSLm (n ≥ 2, m ≥ 2) over division rings. It was found that such groups can be isomorphic only if n = m; the division rings are isomorphic or anti-isomorphic, except for the following groups:

PSL(2,F7) and PSL(3,F2); PSL(2, F4) and PSL(2,F5).

The idea is based on a deepening of the classical Hua's approach. This problem has been solved independently by H. Ren, Z. Wan and X. Wu using a different way

Keywords

20G3516A39
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 5 , 01 October 1993 , pp. 997 - 1008
Copyright
Copyright © Canadian Mathematical Society 1993

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