Good action of a nilpotent group with regular orbits

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ERCAN G., GÜLOĞLU İ. Ş.

COMMUNICATIONS IN ALGEBRA, vol.50, no.10, pp.4191-4194, 2022 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 50 Issue: 10
  • Publication Date: 2022
  • Doi Number: 10.1080/00927872.2022.2058008
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.4191-4194
  • Keywords: Fitting height, good action, nilpotent group, regular orbit
  • Open Archive Collection: AVESIS Open Access Collection
  • Middle East Technical University Affiliated: Yes

Abstract

Suppose that A is a finite nilpotent group of odd order having a good action, in the sense of [1], on the group G of odd order. Under some additional assumptions we prove that the Fitting height of G is bounded above by the sum of the numbers of primes dividing vertical bar A vertical bar and vertical bar C-G(A)vertical bar counted with multiplicities.