Characterization of the groups $D_{p+1}(2)$ and $D_{p+1}(3)$ using order components

Mohammad Reza Darafsheh

doi:10.4134/JKMS.2010.47.2.311

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J. Korean Math. Soc. 2010; 47(2): 311-329

Printed March 1, 2010

https://doi.org/10.4134/JKMS.2010.47.2.311

Characterization of the groups $D_{p+1}(2)$ and $D_{p+1}(3)$ using order components

Mohammad Reza Darafsheh

University of Tehran

Abstract

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Abstract

In this paper we will prove that the groups $D_{p+1}(2)$ and $D_{p+1}(3),$ where $p$ is an odd prime number, are uniquely determined by their sets of order components. A main consequence of our result is the validity of Thompson's conjecture for the groups $D_{p+1}(2)$ and $D_{p+1}(3)$.

Keywords: prime graph, order component, linear group

MSC numbers: 20D05, 20D60