eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2016-06-01
5
2
1
6
10.22108/ijgt.2016.7265
7265
Finite BCI-groups are solvable
Majid Arezoomand
arezoomand@math.iut.ac.ir
1
Bijan Taeri
b.taeri@cc.iut.ac.ir
2
Isfahan University of Technology
Isfahan University of Technology
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 $Gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid xin G, sin S}$. 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 $gin G$ and $alphain Aut(G)$. 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.
http://ijgt.ui.ac.ir/article_7265_5d7f9ab8bf8b6c396bfac5b1e7a5f461.pdf
Bi-Cayley graph
graph isomorphism
solvable group
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2016-06-01
5
2
7
24
10.22108/ijgt.2016.6250
6250
On Fitting groups whose proper subgroups are solvable
Ali Asar
aliasar@gazi.edu.tr
1
No affiliation
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.
http://ijgt.ui.ac.ir/article_6250_2731890be3cf198c7b911db53915fe36.pdf
Fitting group
normalizer
Engel condition
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2016-06-01
5
2
25
40
10.22108/ijgt.2016.6803
6803
On the free profinite products of profinite groups with commuting subgroups
Gilbert Mantika
gilbertmantika@yahoo.fr
1
Daniel Tieudjo
tieudjo@yahoo.com
2
Ecole Normale Suprieure The University of Maroua
The University of Ngaoundere
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.
http://ijgt.ui.ac.ir/article_6803_7c53bf5b29e9c1a021ea9b09dbacc42f.pdf
profinite groups
free constructions of (abstract) groups
free constructions of profinite groups
profinite completions
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2016-06-01
5
2
41
59
10.22108/ijgt.2016.8047
8047
On a group of the form $3^{7}{:}Sp(6,2)$
Ayoub Basheer
ayoubbasheer@gmail.com
1
Jamshid Moori
jamshid.moori@nwu.ac.za
2
North-West University (Mafikeng Campus)
North-West University (Mafikeng Campus)
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 $118times 118 mathbb{C}$-valued matrix, is available in the PhD thesis of the first author, which could be accessed online.
http://ijgt.ui.ac.ir/article_8047_1036b50f7753526ad20d28c67a134790.pdf
Group extensions
symplectic group
character table
inertia groups
Fischer matrices
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2016-06-01
5
2
61
74
10.22108/ijgt.2016.8233
8233
Characterization of some simple $K_4$-groups by some irreducible complex character degrees
Somayeh Heydari
s.heydari.math@gmail.com
1
Neda Ahanjideh
ahanjidn@gmail.com
2
Shahrekord University
Shahrekord university
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.
http://ijgt.ui.ac.ir/article_8233_5d70030b4ccf190d176d5887cd3d551b.pdf
Irreducible complex character degree
Finite simple $K_4$-group
Schur multiplier
normal minimal subgroup