Recognition by spectrum for finite simple linear groups of small dimensions over fields of characteristic 2 |
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| Authors: | A V Vasilyev M A Grechkoseeva |
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| Institution: | (1) Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia;(2) Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia |
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| Abstract: | Two groups are said to be isospectral if they share the same set of element orders. For every finite simple linear group L
of dimension n over an arbitrary field of characteristic 2, we prove that any finite group G isospectral to L is isomorphic
to an automorphic extension of L. An explicit formula is derived for the number of isomorphism classes of finite groups that
are isospectral to L. This account is a continuation of the second author's previous paper where a similar result was established
for finite simple linear groups L in a sufficiently large dimension (n > 26), and so here we confine ourselves to groups of
dimension at most 26.
Supported by RFBR (project Nos. 08-01-00322 and 06-01-39001), by SB RAS (Integration Project No. 2006.1.2), and by the Council
for Grants (under RF President) and State Aid of Leading Scientific Schools (grant NSh-344.2008.1) and Young Doctors and Candidates
of Science (grants MD-2848.2007.1 and MK-377.2008.1).
Translated from Algebra i Logika, Vol. 47, No. 5, pp. 558–570, September–October, 2008. |
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| Keywords: | finite simple group linear group order of element spectrum of group recognition by spectrum |
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