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Title: On finite groups having perfect order subsets
Authors: Das, Ashish Kumar
Keywords: finite groups, semidirect product, divisibility, primes
20D60, 11A41, 11Z05
Issue Date: 2009
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.
ISSN: 1312-8868
Appears in Collections:NEHU Journal Volume 1, Issue No: 1, (January 2003)

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