On table algebras and applications to finite group theory

Order evaluation of products of subsets in finite groups and its applications. II

“…Part 9) is known due to R. Brauer (see [4]). The detailed structure of G satisfying part 1) is known by [1]. In [1] it was shown that there is no finite group satisfying part 2).…”

“…Parts 3)-5), 7)-9) and 11) were open problems; a few of them were mentioned in [1]. Part 6) was proved in [1] by using CFSG. Part 9) is known due to R. Brauer (see [4]).…”

“…Parts 1) and 2) are known by [1]. Parts 3)-5), 7)-9) and 11) were open problems; a few of them were mentioned in [1].…”

Modular Data: The Algebraic Combinatorics of Conformal Field Theory

“…. , x n }, ' * ' given by complex conjugation, and structure constants N k i j = Tr(|α| 2 x i x j x k ) ∈ Q given by ordinary multiplication and addition: x i x j = k N k i j x k . Call the resulting fusion-like algebra K(β).…”

“…That is to say, their axiomatic systems are similar. In particular, a generalised fusion algebra is a table algebra [2], with structure constants in Q and normalised appropriately; a fusion algebra obeys in addition a strong self-duality. However, the exploration of an axiomatic system is influenced not merely by its intrinsic nature (i.e.…”