On finite groups having perfect order subsets
Date
2009
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Hikari Ltd
Abstract
A finite group G is said to be a POS-group if for each x in G the
cardinality of the set {y ∈ 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 An, n ≥ 3, is not a POS-group.
Description
Keywords
finite groups, semidirect product, divisibility, primes, 20D60, 11A41, 11Z05