Carter subgroups and Fitting heights of finite groups

Wenbin Guo, E. P. Vdovin

Research output: Contribution to journalArticlepeer-review

Abstract

Let G be a finite group possessing a Carter subgroup K. Denote by (Formula presented.) the Fitting height of G, by (Formula presented.) the generalized Fitting height of G, and by (Formula presented.) the number of composition factors of K, that is, the number of prime divisors of the order of K with multiplicities. In 1969, E. C. Dade proved that if G is solvable, then (Formula presented.) is bounded in terms of (Formula presented.). In this paper, we show that (Formula presented.) is bounded in terms of (Formula presented.) as well.

Original languageEnglish
Pages (from-to)427-432
Number of pages6
JournalArchiv der Mathematik
Volume110
Issue number5
DOIs
Publication statusPublished - 1 May 2018

Keywords

  • Carter subgroup
  • Finite group
  • Generalized Fitting height
  • Generalized Fitting subgroup

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