University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
5
2
2016
06
01
Finite BCI-groups are solvable
1
6
EN
Majid
Arezoomand
Isfahan University of Technology
arezoomand@math.iut.ac.ir
Bijan
Taeri
Isfahan University of Technology
b.taeri@cc.iut.ac.ir
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.
Bi-Cayley graph,graph isomorphism,solvable group
http://ijgt.ui.ac.ir/article_7265.html
http://ijgt.ui.ac.ir/article_7265_5d7f9ab8bf8b6c396bfac5b1e7a5f461.pdf
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
5
2
2016
06
01
On Fitting groups whose proper subgroups are solvable
7
24
EN
Ali
Osman
Asar
No affiliation
aliasar@gazi.edu.tr
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.
Fitting group,normalizer,Engel condition
http://ijgt.ui.ac.ir/article_6250.html
http://ijgt.ui.ac.ir/article_6250_df2bd4ba078b0e5495d4b876a1609494.pdf
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
5
2
2016
06
01
On the free profinite products of profinite groups with commuting subgroups
25
40
EN
Gilbert
Mantika
Ecole Normale Suprieure
The University of Maroua
gilbertmantika@yahoo.fr
Daniel
Tieudjo
The University of Ngaoundere
tieudjo@yahoo.com
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.
profinite groups,free constructions of (abstract) groups,free constructions of profinite groups,profinite completions
http://ijgt.ui.ac.ir/article_6803.html
http://ijgt.ui.ac.ir/article_6803_7c53bf5b29e9c1a021ea9b09dbacc42f.pdf
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
5
2
2016
06
01
On a group of the form $3^{7}{:}Sp(6,2)$
41
59
EN
Ayoub
Basheer
North-West University (Mafikeng Campus)
ayoubbasheer@gmail.com
Jamshid
Moori
North-West University (Mafikeng Campus)
jamshid.moori@nwu.ac.za
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.
Group extensions,symplectic group,character table,inertia groups,Fischer matrices
http://ijgt.ui.ac.ir/article_8047.html
http://ijgt.ui.ac.ir/article_8047_1036b50f7753526ad20d28c67a134790.pdf
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
5
2
2016
06
01
Characterization of some simple $K_4$-groups by some irreducible complex character degrees
61
74
EN
Somayeh
Heydari
Shahrekord University
s.heydari.math@gmail.com
Neda
Ahanjideh
Shahrekord university
ahanjidn@gmail.com
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.
Irreducible complex character degree,Finite simple $K_4$-group,Schur multiplier,normal minimal subgroup
http://ijgt.ui.ac.ir/article_8233.html
http://ijgt.ui.ac.ir/article_8233_5d70030b4ccf190d176d5887cd3d551b.pdf