We prove that finite groups have the same complex character tables iff the group algebras are twisted forms of each other as Drinfel'd quasi-bialgebras or iff there is non-associative bi-Galois algebra over these groups. The interpretations of class-preserving automorphisms and permutation representations with the same character in terms of Drinfel'd algebras are also given.

In this paper, we prove a few facts and some cardinal properties of the space permutation degree introduced in [6]. More precisely, that if productXn is Lindel?f (resp. locally Lindel?f) space, then SPnX also Lindel?f). We product Xn weakly Moreover, investigate preservation network weight, ?-character local density topological spaces by functor G-permutation degree. It proved preserves infinit...

In this note a combinatorial character formula related to the symmetric group is generalized to an arbitrary finite Weyl group. 1 The Case of the Symmetric Group The length l(π) of a permutation π ∈ Sn is the number of inversions of π, i.e., the number of pairs (i, j) with 1 ≤ i < j ≤ n and π(i) > π(j). For any permutation π ∈ Sn let m(π) be defined as (1) m(π) := 

For any set representation (permutation representation) of the symmetric group Sn, we give combinatorial interpretation for coefficients of its Frobenius character expanded in the basis of monomial symmetric functions.

For any set representation (permutation representation) of the symmetric group Sn, we give combinatorial interpretation for coefficients of its Frobenius character expanded in the basis of monomial symmetric functions.

Let G be a transitive permutation group acting on a finite set E and let P be the stabilizer in G of a point in E. We say that G is primitive rank 3 on E if P is maximal in G and P has exactly three orbits on E. For any subgroup H of G, we denote by 1H the permutation character (or permutation module) over C of G on the cosets G/H. Let H and K be subgroups of G. We say 1H 6 1 G K if 1 G K − 1 G...

For any partition, the corresponding Specht module is the sub module of permutation module spanned by the poly-tabloids. The Specht modules for a partition of a positive integer n form a complete list of irreducible representations of permutation group of degree n. The Semi-Standard Young Tableau (SSYT), on n -symbols are one type of combinatorial objects occur naturally in many computational p...