In 1896, after correspondence with Dedekind, Frobenius published two papers in which
group character theory was introduced and was used to describe the factorization of the …

For a finite group G we study certain rings (k) G called kS-rings, one for each k≥ 1, where
(1) G is the centraliser ring Z (ℂG) of G. These rings have the property that (k+ 1) G …

A weak Cayley table isomorphism is a bijection φ: G→ H of groups such that φ (xy)∼ φ (x) φ
(y) for all x, y∈ G. Here∼ denotes conjugacy. When G= H the set of all weak Cayley table …

In Frobenius' initial papers on group characters he introduced k-characters in order to give
an algorithm to calculate the irreducible factors of the group determinant. We show how his …

For a finite group G we study certain rings called kS-rings, one for each non-negative integer
k, where the 1-S-ring is the centralizer ring of G. These rings have the property that the (k+ 1) …

ABSTRACT A weak Cayley table isomorphism is a bijection φ: G→ H of groups such that φ
(xy)∼ φ (x) φ (y) for all x, y∈ G. Here∼ denotes conjugacy. When G= H the set of all weak …

We study the class of groups G satisfying the condition that, for every ordered pair x,y∈G,
one of the following is true:(1)~ xy=yx;(2)~ x and y are conjugate;(3)~ x^y=x^-1;(4)~ y^x=y …

The ideas in the initial papers by Frobenius on characters and group determinants are set
out and put into context. It is indicated how the theory goes back to the search for “sums of …

The subject of this chapter is the k-characters χ (k) of a finite group G, and their extensions to
more general objects. These characters are constant on certain subsets of G k, the k …

In Frobenius' initial papers on group characters he introduced k-characters in order to give
an algorithm to calculate the irreducible factors of the group determinant. We show how his …