Krauß, Nora2021-04-202021-04-2020171757439366http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-114299http://elib.uni-stuttgart.de/handle/11682/11429http://dx.doi.org/10.18419/opus-11412The double Burnside R-algebra B_R(G,G) of a finite group G with coefficients in a commutative ring R has been introduced by S. Bouc. It is R-linearly generated by finite (G,G)-bisets, modulo a relation identifying disjoint union and sum. Its multiplication is induced by the tensor product. It contains the bifree double Burnside R-algebra B_R^Delta(G,G) generated by bifree finite (G,G)-bisets. Let S_n denote the symmetric group on n letters. For R in {Q, Z, Z_(2), F_2, Z_(3), F_3}, we calculate B_R(S_3,S_3) and B_R^Delta(S_4,S_4).eninfo:eu-repo/semantics/openAccess510masterThesis