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Sibirsk. Mat. Zh., 2019, Volume 60, Number 1, Pages 162–182 (Mi smj3067)  

On recognizability of $\operatorname{PSU}_3(q)$ by the orders of maximal abelian subgroups

Z. Momen, B. Khosravi

Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

Abstract: Li and Chen in 2012 proved that the simple group $A_1(p^n)$ is uniquely determined by the set of orders of its maximal abelian subgroups. Later the authors proved that if $L=A_2(q)$, where $q$ is not a Mersenne prime, then every finite group with the same orders of maximal abelian subgroups as $L$ is isomorphic to $L$ or an extension of $L$ by a subgroup of the outer automorphism group of $L$. In this paper, we prove that if $L=\operatorname{PSU}_3(q)$, where $q$ is not a Fermat prime, then every finite group with the same set of orders of maximal abelian subgroups as $L$ is an almost simple group with socle $\operatorname{PSU}_3(q)$.

Keywords: simple group, maximal abelian subgroup, characterization, projective special unitary group, prime graph.

DOI: https://doi.org/10.33048/smzh.2019.60.114

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English version:
Siberian Mathematical Journal, 2019, 60:1, 124–139

Bibliographic databases:

UDC: 512.54
MSC: 20D05, 20D60, 20D08
Received: 02.10.2016
Revised: 26.08.2018
Accepted:17.10.2018

Citation: Z. Momen, B. Khosravi, “On recognizability of $\operatorname{PSU}_3(q)$ by the orders of maximal abelian subgroups”, Sibirsk. Mat. Zh., 60:1 (2019), 162–182; Siberian Math. J., 60:1 (2019), 124–139

Citation in format AMSBIB
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\paper On recognizability of $\operatorname{PSU}_3(q)$ by the orders of maximal abelian subgroups
\jour Sibirsk. Mat. Zh.
\yr 2019
\vol 60
\issue 1
\pages 162--182
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\crossref{https://doi.org/10.33048/smzh.2019.60.114}
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\transl
\jour Siberian Math. J.
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\vol 60
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\pages 124--139
\crossref{https://doi.org/10.1134/S0037446619010142}
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