Title of article :
Which elements of a finite group are non-vanishing?
Author/Authors :
Arezoomand M. نويسنده Department of
Mathematical Sciences, Isfahan University
of Technology, P.O. Box 84156-83111, Isfahan, Iran. , Taeri B. نويسنده Department of
Mathematical Sciences, Isfahan University
of Technology, P.O. Box 84156-838111, Isfahan, Iran.
Pages :
10
From page :
1097
To page :
1106
Abstract :
-
Abstract :
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-vanishing elements of a finite group $G$. We show that $gin nv(G)$ if and only if the adjacency matrix of ${rm BCay}(G,T)$, where $T={rm Cl}(g)$ is the conjugacy class of $g$, is non-singular. We prove that if the commutator subgroup of $G$ has prime order $p$, then (1) $gin {rm nv}(G)$ if and only if $|Cl(g)|
Journal title :
Astroparticle Physics
Record number :
2412495
Link To Document :
