On Sylow p-subgroups of finitary permutation groups

Asar A.

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

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1007/s11587-026-01079-8
  • Dergi Adı: Ricerche di Matematica
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Gazi Üniversitesi Adresli: Evet

Özet

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.