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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Ciobanu, Laura / Conder, Marston / Eick, Bettina / Elder, Murray / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura / Lohrey, Markus

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Recognition of 2-dimensional projective linear groups by the group order and the set of numbers of its elements of each order

Alireza Khalili AsboeiORCID iD: http://orcid.org/0000-0002-7518-0347
Published Online: 2018-10-11 | DOI: https://doi.org/10.1515/gcc-2018-0011


In a finite group G, let πe(G) be the set of orders of elements of G, let sk denote the number of elements of order k in G, for each kπe(G), and then let nse(G) be the unordered set {sk:kπe(G)}. In this paper, it is shown that if |G|=|L2(q)| and nse(G)=nse(L2(q)) for some prime-power q, then G is isomorphic to L2(q).

Keywords: Element order; set of the numbers of elements of the same order; projective special linear group

MSC 2010: 20D20; 20D60


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About the article

Received: 2018-06-30

Published Online: 2018-10-11

Published in Print: 2018-11-01

Citation Information: Groups Complexity Cryptology, Volume 10, Issue 2, Pages 111–118, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2018-0011.

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