On subgroups normalized by the base group in monomial groups, and their centralizers
Abstract
A large family of examples for subgroups normalized by the base group in a complete monomial group of finite degree over any group
is given. This is then proven to be a complete characterization of such subgroups in the case of an abelian group
. 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
-group
is needed. In the last part, the results are extended to the case of limit monomial groups.
![H](http://212.189.136.205/plugins/generic/latexRender/cache/c1d9f50f86825a1a2302ec2449c17196.png)
![H](http://212.189.136.205/plugins/generic/latexRender/cache/c1d9f50f86825a1a2302ec2449c17196.png)
![2](http://212.189.136.205/plugins/generic/latexRender/cache/c81e728d9d4c2f636f067f89cc14862c.png)
![H](http://212.189.136.205/plugins/generic/latexRender/cache/c1d9f50f86825a1a2302ec2449c17196.png)
DOI Code:
10.1285/i15900932v40n2p111
Keywords:
Monomial group; Base group; Centralizer; Limit monomial group
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