Which elements of a finite group are non-vanishing?

نویسندگان

  • B. Taeri Department of‎ ‎Mathematical Sciences, Isfahan University‎ ‎of Technology‎, ‎P‎.‎O‎. ‎Box 84156-838111, Isfahan‎, ‎Iran.
  • M. Arezoomand Department of‎ ‎Mathematical Sciences, Isfahan University‎ ‎of Technology‎, ‎P‎.‎O‎. ‎Box 84156-83111, Isfahan‎, ‎Iran.
چکیده مقاله:

‎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)|

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which elements of a finite group are non-vanishing?

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عنوان ژورنال

دوره 42  شماره 5

صفحات  1097- 1106

تاریخ انتشار 2016-11-01

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