Towards the Standard Majorana Representations of 3-Transposition Groups

In this paper, we discuss 3-transposition groups. In particular, we find sizes of maximal symmetric subgroups of these groups, which are in Fischer's 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.