Towards the standard Majorana representations of 3-transposition groups

Abstract

In this paper, we discuss 3-transposition groups. In particular, we find sizes of maximal symmetric subgroups of the groups, which are in Fischer list. In addition, we build faithful representations of symmetric groups in orthogonal, symplectic, and unitary spaces, which fully verify the main result. Thus, we find candidate groups, for which one may be able to build standard Majorana representations.

Submitted to the "Journal of Combinatorial Theory, Series A", currently under review