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3 results

  • ON NONINNER AUTOMORPHISMS OF SOME FINITE P-GROUPS

  • Part of
  • SANDEEP SINGH, ROHIT GARG, HEMANT KALRA
  • Journal:
    Bulletin of the Australian Mathematical Society , First View
    Published online by Cambridge University Press:
    08 October 2024, pp. 1-6
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  • We settle the noninner automorphism conjecture for finite p-groups ($p> 2$) with certain conditions. Also, we give an elementary and short proof of the main result of Ghoraishi [‘On noninner automorphisms of finite nonabelian p-groups’, Bull. Aust. Math. Soc. 89(2) (2014) 202–209].

  • ON NONINNER 2-AUTOMORPHISMS OF FINITE 2-GROUPS

  • Part of
  • ALIREZA ABDOLLAHI, S. MOHSEN GHORAISHI
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 90 / Issue 2 / October 2014
    Published online by Cambridge University Press:
    29 May 2014, pp. 227-231
    Print publication:
    October 2014
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  • Let $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}G$ be a finite 2-group. If $G$ is of coclass 2 or $(G,Z(G))$ is a Camina pair, then $G$ admits a noninner automorphism of order 2 or 4 leaving the Frattini subgroup elementwise fixed.

  • ON THE EXISTENCE OF NONINNER AUTOMORPHISMS OF ORDER TWO IN FINITE 2-GROUPS

  • Part of
  • A. R. JAMALI, M. VISEH
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 87 / Issue 2 / April 2013
    Published online by Cambridge University Press:
    17 September 2012, pp. 278-287
    Print publication:
    April 2013
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  • In this paper we prove that every nonabelian finite 2-group with a cyclic commutator subgroup has a noninner automorphism of order two fixing either Φ(G) or Z(G) elementwise. This, together with a result of Peter Schmid on regular p-groups, extends our result to the class of nonabelian finite p-groups with a cyclic commutator subgroup.