A property of the variety of 2-Engel groups
A property which ensures that a finitely generated hyper-(Abelian-by-finite) group is finite-by-nilpotent
Let be the class of groups satisfying the minimal condition on normal subgroups and let be the class of groups of finite lower central depth, that is groups such that for some positive integer . The main result states that if is a finitely generated hyper-(Abelian-by-finite) group such that for every , there exists a normal subgroup of finite index in satisfying for every , then is finite-by-nilpotent. As a consequence of this result, we prove that a finitely generated hyper-(Abelian-by-finite)...
A radical for free groups
A rank 3 tangent complex of , odd.
A relatively free topological group that is not varietal free
Answering a 1982 question of Sidney A. Morris, we construct a topological group G and a subspace X such that (i) G is algebraically free over X, (ii) G is relatively free over X, that is, every continuous mapping from X to G extends to a unique continuous endomorphism of G, and (iii) G is not a varietal free topological group on X in any variety of topological groups.
A remark about central automorphisms of groups
A remark on the intersection of the conjugates of the base of quasi-HNN groups.
A Residual Property of Certain Free Products.
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 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.