The k-characters are class functions on subsets of G^k called the k-classes of G. For a finite group G, the k-class sums form a basis for a subring of CG^k, which we call the k-S-ring of G、and we think of these rings...The k-characters are class functions on subsets of G^k called the k-classes of G. For a finite group G, the k-class sums form a basis for a subring of CG^k, which we call the k-S-ring of G、and we think of these rings as generalized centralizer rings. We show that for a finite group G the 3-S-ring determines G. More specifically, the group characters and set products of certain 3-classes of G, which we call “uniform 3-classes", determine G.展开更多
文摘The k-characters are class functions on subsets of G^k called the k-classes of G. For a finite group G, the k-class sums form a basis for a subring of CG^k, which we call the k-S-ring of G、and we think of these rings as generalized centralizer rings. We show that for a finite group G the 3-S-ring determines G. More specifically, the group characters and set products of certain 3-classes of G, which we call “uniform 3-classes", determine G.
