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


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.

DOI Code: 10.1285/i15900932v40n2p111

Keywords: Monomial group; Base group; Centralizer; Limit monomial group

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