The set of ergodic groups of universal algebras
The set of hypergroups with operators which are constructed from a set with two elements
The set of minimal distances in Krull monoids
Let H be a Krull monoid with class group G. Then every nonunit a ∈ H can be written as a finite product of atoms, say . The set (a) of all possible factorization lengths k is called the set of lengths of a. If G is finite, then there is a constant M ∈ ℕ such that all sets of lengths are almost arithmetical multiprogressions with bound M and with difference d ∈ Δ*(H), where Δ*(H) denotes the set of minimal distances of H. We show that max Δ*(H) ≤ maxexp(G)-2,(G)-1 and that equality holds if every...
The shape of a group---connections between shape theory and the homology of groups
The situation of in the sporadic simple group He
The size of an annihilator in a factorization.
The skeleton of a reduced word and a correspondence of Edelman and Green.
The Skew-Hyperbolic Motion Group of the Quaternion Plane.
The small index property for algebras.
The small index property for quadratic spaces.
The small Ree group and related graph
Let be a finite group. The main supergraph is a graph with vertex set in which two vertices and are adjacent if and only if or . In this paper, we will show that if and only if . As a main consequence of our result we conclude that Thompson’s problem is true for the small Ree group .
The smallest ideals in the two natural products on ßS.
The Soluble Length of Soluble Linear Groups.
The special circulant matrix and units in group rings.
The split building of a reductive group.
The splitting length of mixed Abelian groups of rank one
The splitting of the tensor product of two mixed abelian groups of rank one
The square model for random groups
We introduce a new random group model called the square model: we quotient a free group on n generators by a random set of relations, each of which is a reduced word of length 4. We prove that, just as in the Gromov model, for densities > 1/2 a random group in the square model is trivial with overwhelming probability and for densities < 1/2 a random group is hyperbolic with overwhelming probability. Moreover, we show that for densities d < 1/3 a random group in the square model does not...
The Stanley-Féray-Śniady formula for the generalized characters of the symmetric group
We show that the explicit formula of Stanley-Féray-Śniady for the characters of the symmetric group has a natural extension to the generalized characters. These are the spherical functions of the unbalanced Gel’fand pair .
The Steinberg Function of a Finite Lie Algebra.