A Short Proof of a Theorem of Burns.
A simple construction for the Fischer-Griess monster group.
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.
A simple proof of Vinogradov’s theorem on the orderability of the free product of -groups
A Specialization Theorem for Certain Weyl Group Representations and an Application to the Green Polynomials of Unitary Groups.
A spelling theorem for staggered generalized 2-complexes, with applications.
A survey on just-non- groups.
A theorem on groups
A Transfer Theorem for Small Primes.
A tropical view on Bruhat-Tits buildings and their compactifications
We relate some features of Bruhat-Tits buildings and their compactifications to tropical geometry. If G is a semisimple group over a suitable non-Archimedean field, the stabilizers of points in the Bruhat-Tits building of G and in some of its compactifications are described by tropical linear algebra. The compactifications we consider arise from algebraic representations of G. We show that the fan which is used to compactify an apartment in this theory is given by the weight polytope of the representation...
A version of Brauer’s theorem for integer central functions
In this article we prove an effective version of the classical Brauer’s Theorem for integer class functions on finite groups.
A very short proof of Forester's rigidity result.
A weak type (1,1) estimate for a maximal operator on a group of isometries of a homogeneous tree
We give a simple proof of a result of R. Rochberg and M. H. Taibleson that various maximal operators on a homogeneous tree, including the Hardy-Littlewood and spherical maximal operators, are of weak type (1,1). This result extends to corresponding maximal operators on a transitive group of isometries of the tree, and in particular for (nonabelian finitely generated) free groups.
Abelian groups have/are near Frattini subgroups
The notions of nearly-maximal and near Frattini subgroups considered by J.B. Riles in [20] and the natural related notions are characterized for abelian groups.
Abelian Normal Subgroups of M-Groups.
Abelian profinite groups
Abelian quasinormal subgroups of groups
Let be any group and let be an abelian quasinormal subgroup of . If is any positive integer, either odd or divisible by , then we prove that the subgroup is also quasinormal in .
Abelian subgroup separability of some one-relator groups.
Abelian subgroups of polycyclic groups.
Abelova cena v roce 2008 udělena za objevy v teorii neabelovských grup