Abstract
Let G be a finite group and let N(G) denote the set of conjugacy class sizes of G. Thompson’s conjecture states that if G is a centerless group and S is a non-abelian simple group satisfying N(G) = N(S), then G ≅ S. In this paper, we investigate a variation of this conjecture for some symmetric groups under a weaker assumption. In particular, it is shown that G ≅ Sym(p + 1) if and only if |G| = (p + 1)! and G has a special conjugacy class of size (p + 1)!/p, where p > 5 is a prime number. Consequently, if G is a centerless group with N(G) = N(Sym(p + 1)), then G ≅ Sym(p + 1).
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.
