Characterization of \(\text{SL}(2,q)\) by its non-commuting graph.

Abstract: Let

G

be a non-abelian group and

Z (G)

be its center. The non-commuting graph

m a t h c a l A_{G}

of

G

is the graph whose vertex set is

and two vertices are joined by an edge if they do not commute. Let

m a t h r m S L (2, q)

be the special linear group of degree 2 over the finite field of order

q

. In this paper we prove that if

G

is a group such that

m a t h c a l A_{G} c o n g m a t h c a l A_{m a t h r m S L (2, q)}

for some prime power

q g e q 2

, then

G c o n g m a t h r m S L (2, q)

.

Full work available at URL: https://arxiv.org/abs/0808.0377

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