Pure quantitative characterization of linear groups over the binary field

Abstract

The purpose of this paper is to discuss the pure scalar characterization of the automorphism group Aut (L₅(2)) and the linear group L₆(2). It is proved that Aut(L₅(2)) and L₆(2) can be characterized quantitatively by the set of element orders. The main results are obtained by using William’s work on prime graph components of finite groups and Brauer characters in trivializing the possible 2-subgroups.

Keywords

finite group / element order / linear group / characterization / 20D60 / 20D06

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