Limit monomial groups

Bostan, Sezen
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.


Homogeneous monomial groups and centralizers
Kuzucuoğlu, Mahmut; Sushchanskyy, Vitaly I. (2018-01-01)
The construction of homogeneous monomial groups are given and their basic properties are studied. The structure of a centralizer of an element is completely described and the problem of conjugacy of two elements is resolved. Moreover, the classification of homogeneous monomial groups are determined by using the lattice of Steinitz numbers, namely, we prove the following: Let and be two Steinitz numbers. The homogeneous monomial groups sigma(H) and sigma(G) are isomorphic if and only if = and HG provided tha...
Monomial groups
Almaş, Özge; Kuzucuoğlu, Mahmut; Solak, Ebru; Department of Mathematics (2017)
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 ar...
Pamuk, Semra (2014-07-03)
Let G be a finite group and F be a family of subgroups of G closed under conjugation and taking subgroups. We consider the question whether there exists a periodic relative F-projective resolution for Z when F is the family of all subgroups HG with rkHrkG-1. We answer this question negatively by calculating the relative group cohomology FH*(G, ?(2)) where G = Z/2xZ/2 and F is the family of cyclic subgroups of G. To do this calculation we first observe that the relative group cohomology FH*(G, M) can be calc...
The Influence of some embedding properties of subgroups on the structure of a finite group
Kızmaz, Muhammet Yasir; Ercan, Gülin; Department of Mathematics (2018)
In a finite group $G$, a subgroup $H$ is called a $TI$-subgroup if $H$ intersects trivially with distinct conjugates of itself. Suppose that $H$ is a Hall $pi$-subgroup of $G$ which is also a $TI$-subgroup. A famous theorem of Frobenius states that $G$ has a normal $pi$-complement whenever $H$ is self normalizing. In this case, $H$ is called a Frobenius complement and $G$ is said to be a Frobenius group. A first main result in this thesis is the following generalization of Frobenius' Theorem. textbf{Theorem...
Generalized chillingworth classes on subsurface torelli groups
Ünlü Eroğlu, Hatice; Korkmaz, Mustafa; Department of Mathematics (2018)
The Torelli group is the subgroup of the mapping class group that acts trivially on homology. Putman's subsurface Torelli groups are an important construction for working with the Torelli group, as they restore the functoriality essential for the inductive arguments on which mapping class group arguments are invariably based. The other important structure on the Torelli group is the Johnson homomorphism. The contraction of the image of the Johnson homomorphism is the Chillingworth class. In this thesis, a c...
Citation Formats
S. Bostan, “Limit monomial groups,” Ph.D. - Doctoral Program, Middle East Technical University, 2021.