A note on groups with self-normalizing cyclic subgroups

M. Shahryari

A note on groups with self-normalizing cyclic subgroups

Group Theory 2014-07-15 v2

Authors: M. Shahryari

Abstract

In this article, we prove that if all non-trivial cyclic subgroups of a group $G$ are self normalizing and $G$ satisfies the implication $\ o(x)\neq o(y)\Rightarrow o(xy)\neq o(x), o(y),$ for all non-trivial elements $x$ and $y$ , then $G$ is a $p$ -group or simple.

Keywords

finite groups finite group theory wreath product of groups

Cite

@article{arxiv.1405.6518,
  title  = {A note on groups with self-normalizing cyclic subgroups},
  author = {M. Shahryari},
  journal= {arXiv preprint arXiv:1405.6518},
  year   = {2014}
}

Comments

This article is withdrawn, because the main result can be proved in more general frame of TC-groups

Related papers

View all related →