Finite groups having nonnormal TI subgroups

Download

index.pdf

Date

2018-08-01

Author

Kızmaz, Muhammet Yasir

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

181
views

0
downloads

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.

Subject Keywords

Normal complement, Double Frobenius group, TI subgroup, Frobenius group

URI

https://hdl.handle.net/11511/51177

Journal

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION

DOI

https://doi.org/10.1142/s021819671850039x

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

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...
Algebraic curves hermitian lattices and hypergeometric functions Zeytin, Ayberk; Önsiper, Mustafa Hurşit; Department of Mathematics (2011) The aim of this work is to study the interaction between two classical objects of mathematics: the modular group, and the absolute Galois group. The latter acts on the category of finite index subgroups of the modular group. However, it is a task out of reach do understand this action in this generality. We propose a lattice which parametrizes a certain system of ”geometric” elements in this category. This system is setwise invariant under the Galois action, and there is a hope that one can explicitly under...
Prime graphs of solvable groups Ulvi , Muhammed İkbal; Ercan, Gülin; Department of Electrical and Electronics Engineering (2020-8) If $G$ is a finite group, its prime graph $Gamma_G$ is constructed as follows: the vertices are the primes dividing the order of $G$, two vertices $p$ and $q$ are joined by an edge if and only if $G$ contains an element of order $pq$. This thesis is mainly a survey that gives some important results on the prime graphs of solvable groups by presenting their proofs in full detail.
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...
Torsion Generators Of The Twist Subgroup Altunöz, Tülin; Pamuk, Mehmetcik; Yildiz, Oguz (2022-1-01) We show that the twist subgroup of the mapping class group of a closed connected nonorientable surface of genus g >= 13 can be generated by two involutions and an element of order g or g -1 depending on whether 9 is odd or even respectively.

Citation Formats

M. Y. Kızmaz, “Finite groups having nonnormal TI subgroups,” INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, pp. 905–914, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51177.