A rigidity theorem for Möbius groups.
A Root System for the Lyons Group.
A sandwich theorem for monotone additive functions.
A scoop from groups: equational foundations for loops
Groups are usually axiomatized as algebras with an associative binary operation, a two-sided neutral element, and with two-sided inverses. We show in this note that the same simplicity of axioms can be achieved for some of the most important varieties of loops. In particular, we investigate loops of Bol-Moufang type in the underlying variety of magmas with two-sided inverses, and obtain ``group-like'' equational bases for Moufang, Bol and C-loops. We also discuss the case when the inverses are only...
A semigroup approach to wreath-product extensions of Solomon's descent algebras.
A semigroup characterization of dot-depth one languages
A semigroup in function algebra.
A semigroup treatment of some theorems on non-negative matrices
A semigroup-theoretic proof of the law of large numbers.
A semilattice of varieties of completely regular semigroups
Completely regular semigroups are unions of their (maximal) subgroups with the unary operation within their maximal subgroups. As such they form a variety whose lattice of subvarieties is denoted by . We construct a 60-element -subsemilattice and a 38-element sublattice of . The bulk of the paper consists in establishing the necessary joins for which it uses Polák’s theorem.
A short direct characterization of GS-quasigroups
The theorem about the characterization of a GS-quasigroup by means of a commutative group in which there is an automorphism which satisfies certain conditions, is proved directly.
A short proof of a theorem of Brodskii.
A short proof, using graphs and groupoids, is given of Brodskii’s theorem that torsion-free one-relator groups are locally indicable.
A Short Proof of a Theorem of Burns.
A short proof of Eilenberg and Moore’s theorem
In this paper we give a short and simple proof the following theorem of S. Eilenberg and J.C. Moore: the only injective object in the category of groups is the trivial group.
A short proof of Rédei's Theorem.
A simple construction for the Fischer-Griess monster group.
A simple construction of semigroups all of whose subsemigroups are left ideals.
A simple matrix semigroup which is not completely simple.
A simple proof for a theorem of chase
A simple proof of Baer;s and Sato's theorems on lattice-isomorphisms between groups
A simple proof is given of a well-known result of the existance of lattice-isomorphisms between locally nilpotent quaternionfree modular groups and abelian groups.