Abstract
The noncommuting graph ∇(G) of a non-abelian group G is defined as follows. The vertex set of ∇(G) is G\Z(G) where Z(G) denotes the center of G and two vertices x and y are adjacent if and only if xy ≠ yx. It has been conjectured that if P is a finite non-abelian simple group and G is a group such that ∇(P) ≅ ∇(G), then G ≅ P. In the present paper, our aim is to consider this conjecture in the case of finite almost simple groups. In fact, we characterize the projective general linear group PGL (2, q) (q is a prime power), which is also an almost simple group, by its noncommuting graph.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
