数学物理学报(英文版) ›› 2004, Vol. 24 ›› Issue (1): 45-51.

• 论文 • 上一篇    下一篇

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

M. R. Darafsheh;A. R. Moghaddamfar A.R. Zokay   

  1. Department of Mathiematics and Computer Sciences, Faculty of Science, University of Tehran, Tehran, Iran

    Department of Mathematics, K.N.T University of Technology, P.O.Box 16315-1618, Tehran, Iran
  • 出版日期:2004-07-13 发布日期:2004-07-13
  • 基金资助:

    This work has been supported by the Research Institute
    for Fundamental Sciences Tabriz, Iran.

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

M. R. Darafsheh;A. R. Moghaddamfar A.R. Zokay   

  • Online:2004-07-13 Published:2004-07-13
  • Supported by:

    This work has been supported by the Research Institute
    for Fundamental Sciences Tabriz, Iran.

摘要:

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.

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

中图分类号: 

  • 20D05