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Sibirsk. Mat. Zh., 2018, Volume 59, Number 4, Pages 791–813 (Mi smj3010)  

On spectra of almost simple extensions of even-dimensional orthogonal groups

M. A. Grechkoseeva

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: The spectrum of a finite group is the set of the orders of its elements. We consider the problem that arises within the framework of recognition of finite simple groups by spectrum: Determine all finite almost simple groups having the same spectrum as its socle. This problem was solved for all almost simple groups with exception of the case that the socle is a simple even-dimensional orthogonal group over a field of odd characteristic. Here we address this remaining case and determine the almost simple groups in question.
Also we prove that there are infinitely many pairwise nonisomorphic finite groups having the same spectrum as the simple $8$-dimensional symplectic group over a field of characteristic other than 7.

Keywords: almost simple group, orders of elements, recognition by spectrum, quasirecognition.

Funding Agency Grant Number
Russian Science Foundation 14-21-00065
The author was supported by the Russian Science Foundation (Grant 14-21-00065).


DOI: https://doi.org/10.17377/smzh.2018.59.405

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English version:
Siberian Mathematical Journal, 2018, 59:4, 623–640

Bibliographic databases:

Document Type: Article
UDC: 512.542
MSC: 35R30
Received: 02.11.2017

Citation: M. A. Grechkoseeva, “On spectra of almost simple extensions of even-dimensional orthogonal groups”, Sibirsk. Mat. Zh., 59:4 (2018), 791–813; Siberian Math. J., 59:4 (2018), 623–640

Citation in format AMSBIB
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\paper On spectra of almost simple extensions of even-dimensional orthogonal groups
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\vol 59
\issue 4
\pages 791--813
\mathnet{http://mi.mathnet.ru/smj3010}
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\jour Siberian Math. J.
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\vol 59
\issue 4
\pages 623--640
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