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2 results

  • Camina Triples

  • Nabil M. Mlaiki
  • Journal:
    Canadian Mathematical Bulletin / Volume 57 / Issue 1 / 14 March 2014
    Published online by Cambridge University Press:
    20 November 2018, pp. 125-131
    Print publication:
    14 March 2014
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  • In this paper, we study Camina triples. Camina triples are a generalization of Camina pairs, first introduced in 1978 by A. R. Camina. Camina’s work was inspired by the study of Frobenius groups. We show that if $(G,\,N,\,M)$ is a Camina triple, then either $G/N$ is a $p$-group, or $M$ is abelian, or $M$ has a non-trivial nilpotent or Frobenius quotient.

  • A NOTE ON AUTOMORPHISMS OF FINITE p-GROUPS

  • Part of
  • S. MOHSEN GHORAISHI
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 87 / Issue 1 / February 2013
    Published online by Cambridge University Press:
    30 March 2012, pp. 24-26
    Print publication:
    February 2013
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  • Let p be an odd prime and let G be a finite p-group such that xZ(G)⊆xG, for all x∈G∖Z(G), where xG denotes the conjugacy class of x in G. Then G has a noninner automorphism of order p leaving the Frattini subgroup Φ(G) elementwise fixed.