IJPAM: Volume 15, No. 4 (2004)

A CHARACTERIZATION OF $PSU(19,q)$

A. IranmaneshDepartment of Mathematics, Tarbiat Modarres University, P.O. Box 14115-137, Tehran, IRAN
Department of Mathematics
Tarbiat Modarres University
P.O. Box 14115-137, Tehran, IRAN
e-mail: iranmana@modares.ac.ir
and
Institute for Studies in Theoretical Physics and Mathematics
Tehran, IRAN


Abstract.Let $G$ be a finite group. The order of $G$ is the product of coprime positive integers which is called the order components of $G$. It was proved that some non-abelian simple groups are uniquely determined by their order components. As the main result of this paper, we show that the simple groups $PSU(19,q)$ are also uniquely determined by their order components. As corollaries of this result, the validity of a conjecture of J.G. Thompson on $PSU(19,q)$ is obtained.

Received: July 6, 2004

AMS Subject Classification: 20D06, 20D60

Key Words and Phrases: simple group, prime graph, order component, finite group

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 15
Issue: 4