Finite BCI-groups are solvable
Majid
Arezoomand
Isfahan University of Technology
author
Bijan
Taeri
Isfahan University of Technology
author
text
article
2016
eng
Let $S$ be a subset of a finite group $G$. The bi-Cayley graph $BCay(G,S)$ of $G$ with respect to $S$ is an undirected graph with vertex set $G\times\{1,2\}$ and edge set $\{\{(x,1),(sx,2)\}\mid x\in G, \ s\in S\}$. A bi-Cayley graph $BCay(G,S)$ is called a BCI-graph if for any bi-Cayley graph $BCay(G,T)$, whenever $BCay(G,S)\cong BCay(G,T)$ we have $T=gS^\alpha$ for some $g\in G$ and $\alpha\in Aut(G)$. A group $G$ is called a BCI-group if every bi-Cayley graph of $G$ is a BCI-graph. In this paper, we prove that every BCI-group is solvable.
International Journal of Group Theory
University of Isfahan
2251-7650
5
v.
2
no.
2016
1
6
http://ijgt.ui.ac.ir/article_7265_5d7f9ab8bf8b6c396bfac5b1e7a5f461.pdf
dx.doi.org/10.22108/ijgt.2016.7265
On Fitting groups whose proper subgroups are solvable
Ali
Asar
No affiliation
author
text
article
2016
eng
This work is a continuation of [A. O. Asar, On infinitely generated groups whose proper subgroups are solvable, J. Algebra, 399 (2014) 870-886.], where it was shown that a perfect infinitely generated group whose proper subgroups are solvable and in whose homomorphic images normal closures of finitely generated subgroups are residually nilpotent is a Fitting $p$-group for a prime $p$. Thus this work is a study of a Fitting $p$-group whose proper subgroups are solvable. New characterizations and some sufficient conditions for the solvability of such a group are obtained.
International Journal of Group Theory
University of Isfahan
2251-7650
5
v.
2
no.
2016
7
24
http://ijgt.ui.ac.ir/article_6250_2731890be3cf198c7b911db53915fe36.pdf
dx.doi.org/10.22108/ijgt.2016.6250
On the free profinite products of profinite groups with commuting subgroups
Gilbert
Mantika
Ecole Normale Suprieure
The University of Maroua
author
Daniel
Tieudjo
The University of Ngaoundere
author
text
article
2016
eng
In this paper we introduce the construction of free profinite products of profinite groups with commuting subgroups. We study a particular case: the proper free profinite products of profinite groups with commuting subgroups. We prove some conditions for a free profinite product of profinite groups with commuting subgroups to be proper. We derive some consequences. We also compute profinite completions of free products of (abstract) groups with commuting subgroups.
International Journal of Group Theory
University of Isfahan
2251-7650
5
v.
2
no.
2016
25
40
http://ijgt.ui.ac.ir/article_6803_7c53bf5b29e9c1a021ea9b09dbacc42f.pdf
dx.doi.org/10.22108/ijgt.2016.6803
On a group of the form $3^{7}{:}Sp(6,2)$
Ayoub
Basheer
North-West University (Mafikeng Campus)
author
Jamshid
Moori
North-West University (Mafikeng Campus)
author
text
article
2016
eng
The purpose of this paper is the determination of the inertia factors, the computations of the Fischer matrices and the ordinary character table of the split extension $\overline{G}= 3^{7}{:}Sp(6,2)$ by means of Clifford-Fischer Theory. We firstly determine the conjugacy classes of $\overline{G}$ using the coset analysis method. The determination of the inertia factor groups of this extension involved looking at some maximal subgroups of the maximal subgroups of $Sp(6,2).$ The Fischer matrices of $\overline{G}$ are all listed in this paper and their sizes range between 2 and 10. The character table of $\overline{G},$ which is a $118\times 118\ \mathbb{C}$-valued matrix, is available in the PhD thesis of the first author, which could be accessed online.
International Journal of Group Theory
University of Isfahan
2251-7650
5
v.
2
no.
2016
41
59
http://ijgt.ui.ac.ir/article_8047_1036b50f7753526ad20d28c67a134790.pdf
dx.doi.org/10.22108/ijgt.2016.8047
Characterization of some simple $K_4$-groups by some irreducible complex character degrees
Somayeh
Heydari
Shahrekord University
author
Neda
Ahanjideh
Shahrekord university
author
text
article
2016
eng
In this paper, we examine that some finite simple $K_4$-groups can be determined uniquely by their orders and one or two irreducible complex character degrees.
International Journal of Group Theory
University of Isfahan
2251-7650
5
v.
2
no.
2016
61
74
http://ijgt.ui.ac.ir/article_8233_5d70030b4ccf190d176d5887cd3d551b.pdf
dx.doi.org/10.22108/ijgt.2016.8233