A Schur ring approach to supercharacters of adjoint groups and related subgroups - Silva, Tânia Sofia Zaragoza Cotrim (2023)
Using the correspondence between central Schur rings and supercharacter theories for finite groups, we simplify the construction of the standard supercharacter theory for adjoint groups of finite radical rings. If the radical ring R is of odd characteristic and is endowed with an anti-involution σ, we define a supercharacter theory for the subgroup of the adjoint group R◦ , R◦ σ , consisting of elements fixed by σ. This theory extends the one previously defined in [9], when R is a nilpotent algebra over a finite field.