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