A property equivalent to commutativity for infinite groups
A property equivalent to permutability for groups
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 spelling theorem for staggered generalized 2-complexes, with applications.
A Strengthened Freiheitssatz.
Abelian subgroup separability of some one-relator groups.
About presentations of braid groups and their generalizations
In the paper we give a survey of rather new notions and results which generalize classical ones in the theory of braids. Among such notions are various inverse monoids of partial braids. We also observe presentations different from standard Artin presentation for generalizations of braids. Namely, we consider presentations with small number of generators, Sergiescu graph-presentations and Birman-Ko-Lee presentation. The work of V.~V.~Chaynikov on the word and conjugacy problems for the singular...
Active sums I.
Given a generating family F of subgroups of a group G closed under conjugation and with partial order compatible with inclusion, a new group S can be constructed, taking into account the multiplication in the subgroups and their mutual actions given by conjugation. The group S is called the active sum of F, has G as a homomorph and is such that S/Z(S) ≅ G/Z(G) where Z denotes the center.The basic question we investigate in this paper is: when is the active sum S of the family F isomorphic to the...
Algebraic groups with a distinguished conjugacy class.
Algorithmic problems related to the direct product of groups.
Almost all one-relator groups with at least three generators are residually finite
We prove that with probability tending to 1, a one-relator group with at least three generators and the relator of length is residually finite, is a virtually residually (finite -)group for all sufficiently large , and is coherent. The proof uses both combinatorial group theory and non-trivial results about Brownian motions.
Almost finitely presented soluble groups.
Amalgamated products and finitely presented groups.
Amenability of linear-activity automaton groups
We prove that every linear-activity automaton group is amenable. The proof is based on showing that a random walk on a specially constructed degree 1 automaton group – the mother group – has asymptotic entropy 0. Our result answers an open question by Nekrashevych in the Kourovka notebook, and gives a partial answer to a question of Sidki.
An alternative proof that the Fibonacci group is infinite.
An analog of the Baer-Suzuki theorem for infinite groups.
An analytic interpretation of real dimension subgroups.
An elementary approach to the mapping class group of a surface.
An existence lemma for groups generated by 3-transpositions.