A group is called quasihamiltonian if all its subgroups are permutable, and we say that a subgroup Q of a group G is permutably embedded in G if < Q, g > is quasihamiltonian for each element g of G. It is proved here that if a group G contains a permutably embedded normal subgroup Q such that G/Q is Cernikov, then G has a quasihamiltonian subgroup of finite index; moreover, if G is periodic, then it contains a Cernikov normal subgroup N such that G/N is quasihamiltonian. This result should be compared with theorems of Cernikov and Schlette stating that if a group G is Cernikov over its centre, then G is abelian-by-finite and its commutator subgroup is Cernikov.

Groups with a large permutably embedded subgroup

De Falco Maria;de Giovanni Francesco;C. Musella
2022

Abstract

A group is called quasihamiltonian if all its subgroups are permutable, and we say that a subgroup Q of a group G is permutably embedded in G if < Q, g > is quasihamiltonian for each element g of G. It is proved here that if a group G contains a permutably embedded normal subgroup Q such that G/Q is Cernikov, then G has a quasihamiltonian subgroup of finite index; moreover, if G is periodic, then it contains a Cernikov normal subgroup N such that G/N is quasihamiltonian. This result should be compared with theorems of Cernikov and Schlette stating that if a group G is Cernikov over its centre, then G is abelian-by-finite and its commutator subgroup is Cernikov.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/901384
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact