Pos Groups Revisited

Ashish Kumar Das

Pos Groups Revisited

Group Theory 2009-03-23 v2 Number Theory

Authors: Ashish Kumar Das

Abstract

A finite group $G$ is said to be a POS-group if for each $x$ in $G$ the cardinality of the set $\{y \in G | o(y) =o(x)\}$ is a divisor of the order of $G$ . In this paper we study some of the properties of arbitrary POS-groups, and construct a couple of new families of nonabelian POS-groups. We also prove that the alternating group $A_n$ , $n \ge 3$ , is not a POS-group.

Keywords

finite group theory finite groups

Cite

@article{arxiv.0902.3620,
  title  = {Pos Groups Revisited},
  author = {Ashish Kumar Das},
  journal= {arXiv preprint arXiv:0902.3620},
  year   = {2009}
}

Comments

9 pages, new results and new references included

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