Vol. 4, No. 3, 2011

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On three questions concerning groups with perfect order subsets

Lenny Jones and Kelly Toppin

Vol. 4 (2011), No. 3, 251–261

In a finite group, an order subset is a maximal set of elements of the same order. We discuss three questions about finite groups G having the property that the cardinalities of all order subsets of G divide the order of G. We provide a new proof to one of these questions and evidence to support answers to the other two questions.

perfect order subsets, abelian group, symmetric group
Mathematical Subject Classification 2000
Primary: 20F99, 11Y05
Secondary: 11A51
Received: 23 July 2010
Accepted: 15 June 2011
Published: 13 March 2012

Communicated by Kenneth S. Berenhaut
Lenny Jones
Department of Mathematics
Shippensburg University
1871 Old Main Drive
Shippensburg, PA 17257
United States
Kelly Toppin
Department of Mathematics
Shippensburg University
Shippensburg, PA 17257
United States