B. Taeri

Department of Mathematical Sciences‎, ‎Isfahan University of Technology‎, ‎Isfahan 84156-83111‎, ‎Iran‎.

[ 1 ] - NSE characterization of some linear groups

‎For a finite group $G$‎, ‎let $nse(G)={m_kmid kinpi_e(G)}$‎, ‎where $m_k$ is the number of elements of order $k$ in $G$‎ ‎and $pi_{e}(G)$ is the set of element orders of $G$‎. ‎In this paper‎, ‎we prove that $Gcong L_m(2)$ if and only if $pmid |G|$ and $nse(G)=nse(L_m(2))$‎, ‎where $min {n,n+1}$ and $2^n-1=p$ is a prime number.

[ 2 ] - Which elements of a finite group are non-vanishing?

‎Let $G$ be a finite group‎. ‎An element $gin G$ is called non-vanishing‎, ‎if for‎ ‎every irreducible complex character $chi$ of $G$‎, ‎$chi(g)neq 0$‎. ‎The bi-Cayley graph ${rm BCay}(G,T)$ of $G$ with respect to a subset $Tsubseteq G$‎, ‎is an undirected graph with‎ ‎vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(tx,2)}mid xin G‎, ‎ tin T}$‎. ‎Let ${rm nv}(G)$ be the set‎ ‎of all non-vanishi...

[ 3 ] - On the planarity of a graph related to the join of subgroups of a finite group

‎Let $G$ be a finite group which is not a cyclic $p$-group‎, ‎$p$ a prime number‎. ‎We define an undirected simple graph $Delta(G)$ whose‎ ‎vertices are the proper subgroups of $G$, which are not contained in the‎ ‎Frattini subgroup of $G$ and two vertices $H$ and $K$ are joined by an edge‎ ‎if and only if $G=langle H‎ , ‎Krangle$‎. ‎In this paper we classify finite groups with planar graph‎. ‎...

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