Monomial groups

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2017

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Almaş, Özge

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A group G is called a permutation group if it is a subgroup of a symmetric group on aset Ω. GiscalledalineargroupifitisasubgroupofthegenerallineargroupGL(n, F) for a ﬁeld F. Monomial groups are generalization of permutation groups and restriction of linear groups. In matrix terminology, monomial groups of degree n over a group H are the n× n invertible matrices in which each row and each column contains only one element of H all the other entries are zero. Basic properties of ﬁnite degree monomial groups are studied by Ore in [2]. Inﬁnite degree monomial groups over an arbitrary group H is studied by Crouch in [1]. This thesis is a survey of the Crouch paper, in particular we will give a complete classiﬁcation of the structure of centralizers of arbitrary elements in complete monomial groups Σ(H;B,B+,B+) and conjugacy of the elements in Σ(H;B,B+,B+).

Subject Keywords

Monomial groups., Permutation groups.

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http://etd.lib.metu.edu.tr/upload/12621243/index.pdf
https://hdl.handle.net/11511/26916

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

Ö. Almaş, “Monomial groups,” M.S. - Master of Science, Middle East Technical University, 2017.