On Sylow p-subgroups of finitary permutation groups

Asar A.

Ricerche di Matematica, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2026
  • Doi Number: 10.1007/s11587-026-01079-8
  • Journal Name: Ricerche di Matematica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Gazi University Affiliated: Yes

Abstract

In this work it is shown that, for a prime number p, a totally imprimitive group of finitary permutations on an infinite set has either a unique Sylow p-subgroup or the cardinality of its Sylow p-subgroups is equal to 2ℵ0. If in particular a Sylow p-subgroup of the group is transitive, then either the group is a p-group or the cardinality of its transitive Sylow p-subgroups is equal to 2ℵ0. It follows from this that the cardinality of the Sylow p-subgroups of the finitary symmetric group on a infinite set is equal to 2ℵ0.