Pos Groups Revisited

Details Pos Groups Revisited Pos Groups Revisited

2009-02-20

arxiv.org/abs/0902.3620v2

Mathematics

Group Theory

9 pages, new results and new references included

Scientific paper

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.

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