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Limit monomial groups
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12626254.pdf
Date
2021-3-03
Author
Bostan, Sezen
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In this thesis, monomial groups, which are obtained by using strictly diagonal embeddings of complete monomial groups over a group of finite degree, are studied. The direct limit of complete monomial groups of finite degree with strictly diagonal embeddings is called limit monomial group . Normal subgroup structure of limit monomial groups over abelian groups is studied. We classified all subgroups of rational numbers, containing integers, by using base subgroup of limit monomial groups. We also studied the splitting problem in limit monomial groups. Using the facts in the case of complete monomial groups of finite degree, we prove that limit monomial group splits over its base group and there are uncountably many complements of the base group in limit monomial group, depending on the group and Steinitz number. Moreover, to classify all complements of the base group up to conjugacy, we prove that the group, over which limit monomial group set, contains diagonal direct limit of finite symmetric groups.
Subject Keywords
Monomial group
,
Direct limit
,
Strictly diagonal embedding
,
Splitting
URI
https://hdl.handle.net/11511/89631
Collections
Graduate School of Natural and Applied Sciences, Thesis
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S. Bostan, “Limit monomial groups,” Ph.D. - Doctoral Program, Middle East Technical University, 2021.