Homogeneous monomial groups and centralizers

Kuzucuoğlu, Mahmut
Sushchanskyy, Vitaly I.
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 that the splittings of sigma(H) and sigma(G) are regular.


Limit monomial groups
Bostan, Sezen; Kuzucuoğlu, Mahmut; Department of Mathematics (2021-3-03)
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...
Finite groups having nonnormal TI subgroups
Kızmaz, Muhammet Yasir (2018-08-01)
In the present paper, the structure of a finite group G having a nonnormal T.I. subgroup H which is also a Hall pi-subgroup is studied. As a generalization of a result due to Gow, we prove that H is a Frobenius complement whenever G is pi-separable. This is achieved by obtaining the fact that Hall T.I. subgroups are conjugate in a finite group. We also prove two theorems about normal complements one of which generalizes a classical result of Frobenius.
Universal groups of intermediate growth and their invariant random subgroups
Benli, Mustafa Gökhan; Nagnibeda, Tatiana (2015-07-01)
We exhibit examples of groups of intermediate growth with ergodic continuous invariant random subgroups. The examples are the universal groups associated with a family of groups of intermediate growth.
Centralizers of finite subgroups in Hall's universal group
Kegel, Otto H.; Kuzucuoğlu, Mahmut (2017-01-01)
The structure of the centralizers of elements and finite abelian subgroups in Hall's universal group is studied by B. Hartley by using the property of existential closed structure of Hall's universal group in the class of locally finite groups. The structure of the centralizers of arbitrary finite subgroups were an open question for a long time. Here by using basic group theory and the construction of P. Hall we give a complete description of the structure of centralizers of arbitrary finite subgroups in Ha...
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...
Citation Formats
M. Kuzucuoğlu and V. I. Sushchanskyy, “Homogeneous monomial groups and centralizers,” COMMUNICATIONS IN ALGEBRA, pp. 597–609, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38696.