On groups with perfect order subsets

Kevin Ford, Sergei Konyagin, Florian Luca

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)3-18
Number of pages16
JournalMoscow Journal of Combinatorics and Number Theory
Issue number4
StatePublished - 2012


  • Abelian groups
  • Pratt trees
  • primes

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Algebra and Number Theory


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