3 citations · 14 across the 8 of their papers we have counts for
12 papers
The Burnside problem for odd exponents
Agatha Atkarskaya, Eliyahu Rips, Katrin Tent
We show that the free Burnside groups are infinite for and odd , the best currently known lower bound for the exponent. The proof uses iterated small…
Group-like small cancellation theory for rings
A. Atkarskaya, A. Kanel-Belov, E. Plotkin +1
In the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free gr…
Small cancelation rings
A. Atkarskaya, A. Kanel-Belov, E. Plotkin +1
The theory of small cancellation groups is well known. In this paper we introduce the notion of Group-like Small Cancellation Ring. This is the main result of the paper. We define…
On Products of Closed Subsets in Free Groups
Rita Gitik, Eliyahu Rips
We present examples of closed subsets of a free group such that their product is not closed in the profinite topology. We discuss how to characterize a subset of a free group which…
On Growth of Double Cosets in Hyperbolic Groups
Rita Gitik, Eliyahu Rips
Let be a hyperbolic group, and be subgroups of , and be the growth function of the double cosets . We prove that the behavior of $gr(H,A,B)…
Construction of a quotient ring of in which a binomial is invertible using small cancellation methods
A. Atkarskaya, A. Kanel-Belov, E. Plotkin +1
We apply small cancellation methods originating from group theory to investigate the structure of a quotient ring , where $\mathbb{Z}_2\mathc…