On the number of conjugacy classes of $\pi$-elements in finite groups

Attila Maroti; Hung Ngoc Nguyen

On the number of conjugacy classes of $\pi$-elements in finite groups

Group Theory 2014-01-21 v4

Authors: Attila Maroti , Hung Ngoc Nguyen

Abstract

Let $G$ be a finite group and $\pi$ be a set of primes. We show that if the number of conjugacy classes of $\pi$ -elements in $G$ is larger than $5/8$ times the $\pi$ -part of $|G|$ then $G$ possesses an abelian Hall $\pi$ -subgroup which meets every conjugacy class of $\pi$ -elements in $G$ . This extends and generalizes a result of W. H. Gustafson.

Keywords

finite groups conjugacy classes pi-elements hall pi-subgroup abelian subgroup group theory

Cite

@article{arxiv.1306.0747,
  title  = {On the number of conjugacy classes of $\pi$-elements in finite groups},
  author = {Attila Maroti and Hung Ngoc Nguyen},
  journal= {arXiv preprint arXiv:1306.0747},
  year   = {2014}
}

Comments

7 pages

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