Abstract
The reduced power graph of a group G is a graph whose vertices are the non-identity elements of G, with two vertices connected by an edge if and only if one is a power of the other. Akbari and Ashrafi conjectured that if a non-abelian finite simple group has a connected reduced power graph, then it must be an alternating group. In this paper, we disprove this conjecture by providing a complete description of when the reduced power graphs of PGLn(Fq) are connected for all q and all n≥3. We also provide upper bounds on their diameters and, in case of disconnection, a description of all connected components. Our results have implications for the study of power graphs of other families of groups.
Sign-in/Register to access full text options 
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.
