Involve: A Journal of Mathematics

  • Involve
  • Volume 4, Number 3 (2011), 251-261.

On three questions concerning groups with perfect order subsets

Lenny Jones and Kelly Toppin

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Abstract

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.

Article information

Source
Involve, Volume 4, Number 3 (2011), 251-261.

Dates
Received: 23 July 2010
Accepted: 15 June 2011
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1513733395

Digital Object Identifier
doi:10.2140/involve.2011.4.251

Mathematical Reviews number (MathSciNet)
MR2905226

Zentralblatt MATH identifier
1261.20026

Subjects
Primary: 20F99: None of the above, but in this section 11Y05: Factorization
Secondary: 11A51: Factorization; primality

Keywords
perfect order subsets abelian group symmetric group

Citation

Jones, Lenny; Toppin, Kelly. On three questions concerning groups with perfect order subsets. Involve 4 (2011), no. 3, 251--261. doi:10.2140/involve.2011.4.251. https://projecteuclid.org/euclid.involve/1513733395


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