We study co-Frobenius and more generally quasi-co-Frobenius corings over arbitrary base rings and over PF base rings in particular. We generalize some results about co-Frobenius and quasi-co-Frobenius coalgebras to the case of noncommutative base rings and give several new characterizations for co-Frobenius and more generally quasi-co-Frobenius corings, some of them are new even in the coalgebr...

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.

in this paper, by using of frobenius theorem a relation between lie subalgebras of the lie algebra of a top space t and lie subgroups of t(as a lie group) is determined. as a result we can consider these spaces by their lie algebras. we show that a top space with the finite number of identity elements is a c^{∞} principal fiber bundle, by this method we can characterize top spaces.

We give an explicit description, up to gauge equivalence, of group-theoretical quasi-Hopf algebras. We use this description to compute the Frobenius-Schur indicators for grouptheoretical fusion categories.

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.

We show how the framework of crossed simplicial groups may be used to provide a classification of topological field theories on open cobordism categories defined by reductions of the structure group to a planar Lie group. Such theories are equivalent to algebras equipped with a group action and a non-degenerate trace satisfying certain invariance requirements which generalize the notion of a fr...

The famous Frobenius characteristic map is a bijection from the space of characters of a symmetric group S n to the space of homogeneous symmetric functions of degree n. In this note, we prove a formula for the inverse map. More precisely, we express the generating function for the values of an arbitrary virtual character of S n in terms of the symmetric function which is the Frobenius image of...

Suppose that a finite group G admits a Frobenius group of automorphisms FH with kernel F and complement H such that the fixed-point subgroup of F is trivial: CG(F ) = 1. In this situation various properties of G are shown to be close to the corresponding properties of CG(H). By using Clifford’s theorem it is proved that the order |G| is bounded in terms of |H| and |CG(H)|, the rank of G is boun...

we give a new proof of the well known wedderburn's little theorem (1905) that a finite‎ ‎division ring is commutative‎. ‎we apply the concept of frobenius kernel in frobenius representation theorem in finite group‎ ‎theory to build a proof‎.

Given integers n ≥ 7 and a,b,c with 1 ≤ a,b,c ≤ n − 1 such that a,n − a,b,n − b,c,n − c are pairwise distinct, the (undirected) triple-loop network TLn(a,b,c) is the degree-six graph with vertices 0, 1, 2, . . . ,n − 1 such that each vertex x is adjacent to x ± a, x ± b, and x ± c, where the operation is modulo n. It is known that the maximum order of a connected triple-loop network of the form...