A RECOGNITION OF SIMPLE GROUPS PSL(3, q) BY THEIR ELEMENT ORDERS

Abstract

Abstract:

For any group G, denote by e(G) the set of orders of elements in G. Given
a finite group G, let h(e(G)) be the number of isomorphism classes of finite groups with
the same set e(G) of element orders. A group G is called k-recognizable if h(e(G)) =
k < 1, otherwise G is called non-recognizable. Also a 1-recognizable group is called a
recognizable (or characterizable) group. In this paper the authors show that the simple
groups PSL(3, q), where 3 < q ±2 (mod 5) and (6, (q − 1)/2) = 1, are recognizable.

Key words: Element order;prime graph, projective special linear group

CLC Number:

20D05

M. R. Darafsheh;A. R. Moghaddamfar A.R. Zokay. A RECOGNITION OF SIMPLE GROUPS PSL(3, q) BY THEIR ELEMENT ORDERS[J].Acta mathematica scientia,Series B, 2004, 24(1): 45-51.

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