NILPOTENT LENGTH OF A FINITE SOLVABLE GROUP WITH A FROBENIUS GROUP OF AUTOMORPHISMS

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ERCAN G., GÜLOĞLU İ. Ş., Ogut E.

COMMUNICATIONS IN ALGEBRA, vol.42, no.11, pp.4751-4756, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 11
  • Publication Date: 2014
  • Doi Number: 10.1080/00927872.2013.823776
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.4751-4756
  • Middle East Technical University Affiliated: Yes

Abstract

We prove that a finite solvable group G admitting a Frobenius group FH of automorphisms of coprime order with kernel F and complement H such that [G, F] = G and C-CG(F) (h) = 1 for all nonidentity elements h is an element of H, is of nilpotent length equal to the nilpotent length of the subgroup of fixed points of H.