On abelian group actions with TNI-centralizers


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Ercan G., Guloglu I. S.

COMMUNICATIONS IN ALGEBRA, vol.47, pp.3003-3006, 2019 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47
  • Publication Date: 2019
  • Doi Number: 10.1080/00927872.2018.1549662
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.3003-3006

Abstract

A subgroup H of a group G is said to be a TNI-subgroup if for any Let A be an abelian group acting coprimely on the finite group G by automorphisms in such a way that for all is a solvable TNI-subgroup of G. We prove that G is a solvable group with Fitting length h(G) is at most . In particular whenever is nonnormal. Here, h(G) is the Fitting length of G and is the number of primes dividing A counted with multiplicities.