IJPAM: Volume 63, No. 4 (2010)

THE LARGEST CONJUGACY SIZES AND
SOLVABILITY OF FINITE GROUPS

Liguo He$^1$, Zhe Zhang$^2$, Hong Li$^3$
$^{1,2,3}$Department of Mathematics
Shenyang University of Technology
Shenyang, 110870, P.R. CHINA
$^1$e-mail: [email protected]


Abstract.In this note, it is proved that if the largest conjugacy class size of the finite group $G$ is less than or equal to $19$, then $G$ is solvable. We observe that the largest conjugacy class size of the alternating group $A_5$ of degree $5$ is $20$.

Received: June 20, 2010

AMS Subject Classification: 20C15

Key Words and Phrases: solvable group, conjugacy class size

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 63
Issue: 4