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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
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
\Bibitem{MomKho19} \by Z.~Momen, B.~Khosravi \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 \mathnet{http://mi.mathnet.ru/smj3067} \crossref{https://doi.org/10.33048/smzh.2019.60.114} \elib{http://elibrary.ru/item.asp?id=39129783} \transl \jour Siberian Math. J. \yr 2019 \vol 60 \issue 1 \pages 124--139 \crossref{https://doi.org/10.1134/S0037446619010142} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000464720000014} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85065247395}