On subgroups normalized by the base group in monomial groups, and their centralizers

BOSTAN S., Esposito D.

NOTE DI MATEMATICA, vol.40, no.2, pp.111-127, 2020 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.1285/i15900932v40n2p111
  • Journal Name: NOTE DI MATEMATICA
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.111-127
  • Middle East Technical University Affiliated: Yes

Abstract

A large family of examples for subgroups normalized by the base group in a complete monomial group of finite degree over any group H is given. This is then proven to be a complete characterization of such subgroups in the case of an abelian group H. Centralizer structure for this kind of subgroups, even in the non abelian case, is completely determined. Notably, separate study of the case of elementary abelian 2-group H is needed. In the last part, the results are extended to the case of limit monomial groups.