Abstract
Let G be a non-abelian group and associate a non-commuting graph ∇(G) with G as follows: the vertex set of ∇(G) is G\Z(G) with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity. In this short paper we prove that if G is a finite group with ∇(G) ≅ ∇(M), where M = L 2(q) (q = p n, p is a prime), then G ≅ M.
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References
Williams J S. Prime graph components of finite groups. J Algebra, 1981, 69: 487–513
Bertram E A, Herzog M, Mann A. On a graph related to conjugacy classes of groups. Bull London Math Soc, 1990, 22: 569–575
Moghaddamfar A R, Shi W J, Zhou W, et al. On the noncommuting graph associated with a finite group. Siberian Math J, 2005, 46(2): 325–332
Abdollahi A, Akbari S, Maimani H R. Non-commuting graph of a group. J Algebra, 2006, 298: 468–292
Chen G Y. A new characterization of PSL(2, q). Southeast Asian Bull Math, 1998, 218: 257–263
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Wang, L., Shi, W. A new characterization of L 2(q) by its noncommuting graph. Front. Math. China 2, 143–148 (2007). https://doi.org/10.1007/s11464-007-0010-9
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DOI: https://doi.org/10.1007/s11464-007-0010-9