Supercharacter Theory Constructions Corresponding to Schur Ring Products

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Ramanujan sums as supercharacters (2012, background): “Other recent work on supercharacters concerns connections with Schur rings [23, 25] and with their combinatorial properties [15, 60, 61].”
Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras (2010, methodology): “omorphisms [16], •Finding normal subgroups N⊳Gand grafting together superchararacter theories for the normal subgroup N and for the factor group G/N to get a supercharacter theory for the whole group [22]. This paper will however focus on a technique ﬁrst introduced for algebra groups [16], and then”