Recognition of 2-dimensional projective linear groups by the group order and the set of numbers of its elements of each order-Reference-Cited by-同舟云学术

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

Author:

Khalili Asboei Alireza¹

Affiliation:

1. Department of Mathematics, Farhangian University, Tehran, Iran

Abstract

AbstractIn a finite group G, let

{\pi_{e}(G)}

be the set of orders of elements of G, let

{s_{k}}

denote the number of elements of order k in G, for each

{k\in\pi_{e}(G)}

, and then let

{\operatorname{nse}(G)}

be the unordered set

{\{s_{k}:k\in\pi_{e}(G)\}}

. In this paper, it is shown that if

{\lvert G\rvert=\lvert L_{2}(q)\rvert}

and

{\operatorname{nse}(G)=\operatorname{nse}(L_{2}(q))}

for some prime-power q, then G is isomorphic to

{L_{2}(q)}

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Computer Networks and Communications

Link

Reference46 articles.

1. A characterization of sporadic simple groups by nse and order;J. Algebra Appl.,2013

3. The subgroup structure of finite classical groups in terms of geometric configurations;Surveys in Combinatorics 2005,2005

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