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Paper   IPM / M / 8305
School of Mathematics
  Title:   Characterizability of PSL(p+1,q) by its order component(s)
  Author(s):  Behr. Khosravi (Joint with Bah. Khosravi and Behn. Khosravi)
  Status:   Published
  Journal: Houston J. Math.
  Vol.:  32
  Year:  2006
  Pages:   683-700
  Supported by:  IPM
Order components of a finite group are introduced in Chen (J. Algebra 185 (1996) 184). It was proved that PSL(3, q), where q is an odd prime power, is uniquely determined by its order components (J. Pure and Applied Algebra (2002)). Also in Iranmanesh and et al. (Acta Math. Sinica, English Series (2002)) and (Bull. Austral. Math. Soc. (2002)) it was proved that PSL(3,q) for q = 2n and PSL(5, q) are uniquely determined by their order components. Also it was proved that PSL(p, q) is uniquely determined by its order components (Comm. Algebra (2004)). In this paper we discuss about the characterizability of PSL(p + 1, q) by its order component(s), where p is an odd prime number. In fact we prove that PSL(p + 1, q) is uniquely determined by its order component(s) if and only if (q −1)|(p+1). A main consequence of our results is the validity of Thompson's conjecture for the groups PSL(p + 1, q) where (q −1)|(p + 1).

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