Mathieu groups and its degree prime-power graphs

Abstract

Let cd(G) be the set of irreducible complex character degrees of a finite group G. The degree graph of G related to cd(G) was defined. It was proved many finite simple groups (but not all Mathieu groups) are uniquely determined by their orders and degree graphs. We hope to define a new graph related to cd(G) such that more simple groups can be uniquely determined by their orders and this newly defined graphs. Here a degree prime-power graph is defined and it is proved that all Mathieu groups can be determined uniquely by their orders and degree prime-power graphs.

Keywords:

• Characterization
• degree prime-power graph
• irreducible character
• Mathieu groups

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20C15
• 20D05

Additional information

Funding

This research was supported by grant of National Natural Science Foundation of China (grant no. 11671324).