Monomial groups

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Türkiye

Tezin Onay Tarihi: 2017

Öğrenci: ÖZGE ALMAŞ

Eş Danışman: EBRU SOLAK, MAHMUT KUZUCUOĞLU

Özet:

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+).