Some new characterizations for PGL(2, q)

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DOI:

https://doi.org/10.4067/S0719-06462011000200009

Abstract

Many authors introduced some characterizations for finite groups. In this paper as the main result we prove that the finite group PGL(2, q) is uniquely determined by its noncommuting graph. Also we prove that PGL(2, q) is characterizable by its noncyclic graph. Throughout the proof of these results we prove that PGL(2, q) is uniquely determined by its order components and using this fact we give positive answer to a conjecture of Thompson and another conjecture of Shi and Bi for the group PGL(2, q).

Keywords

Noncommuting graph , prime graph , noncyclic graph , order components
  • B. Khosravi School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran.
  • M. Khatami Dept. of Pure Math., Faculty of Math. and Computer Sci., Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran 15914, Iran.
  • Z. Akhlaghi Dept. of Pure Math., Faculty of Math. and Computer Sci., Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran 15914, Iran.
  • Pages: 151–161
  • Date Published: 2011-06-01
  • Vol. 13 No. 2 (2011): CUBO, A Mathematical Journal

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Published

2011-06-01

How to Cite

[1]
B. Khosravi, M. Khatami, and Z. Akhlaghi, “Some new characterizations for PGL(2, q)”, CUBO, vol. 13, no. 2, pp. 151–161, Jun. 2011.

Issue

Vol. 13 No. 2 (2011): CUBO, A Mathematical Journal

Section

Articles

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