IJPAM: Volume 20, No. 3 (2005)

NOTES ON HUPPERT'S $\rho$-$\sigma$-CONJECTURE

Liguo He
Department of Mathematics
Shenyang University of Technology
Shenyang, 110023, P.R. CHINA
e-mail: heliguo@online.ln.cn


Abstract.For a finite group $G$, in this note, we prove that if $G$ is nilpotent-by-nilpotent, then Huppert's $\rho$-$\sigma$-conjecture is valid for $G$. Also we show that if $G/F(G)$ is nilpotent and Sylow subgroups of $F(G)$ are all non-Abelian, then the conjugacy version of Huppert's $\rho$-$\sigma$-conjecture is true for $G$.

Received: March 5, 2005

AMS Subject Classification: 20C15

Key Words and Phrases: finite group, conjugacy class, Sylow subgroup

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 20
Issue: 3