“School of Mathematics”
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| Paper IPM / M / 11534 |
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| Abstract: | |
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Let G be a non-abelian group. We define the
noncommuting graph ∇(G) of G as follows: its vertex set
is G\Z(G), the set of non-central elements of G, and
two different vertices x and y are joined by an edge if and
only if x and y do not commute as elements of G, i.e.,
[x,y] ≠ 1. We prove that if L ∈ {L4(7), L4(11), L4(13), L4(16), L4(17)} and G is a finite group such that
∇(G) ≅ ∇(L), then G ≅ L.
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