On groups with perfect order subsets

Kevin Ford; Sergei Konyagin; Florian Luca

On groups with perfect order subsets

Kevin Ford, Sergei Konyagin, Florian Luca

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A finite group G is said to have Perfect Order Subsets if for every d, the number of elements of G of order d (if there are any) divides ^G. Answering a question of Finch and Jones from 2002, we prove that if G is Abelian, then such a group has order divisible by 3 except in the case G = Z/2 ^kZ. We also place additional restrictions on the order of such groups.

Original language	English (US)
Pages (from-to)	3-18
Number of pages	16
Journal	Moscow Journal of Combinatorics and Number Theory
Volume	2
Issue number	4
State	Published - 2012

Keywords

Abelian groups
Pratt trees
primes

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Algebra and Number Theory

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On groups with perfect order subsets

Abstract

Keywords

ASJC Scopus subject areas

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