A. Atkarskaya

activity

20182023

most citedThe Burnside problem for odd exponents

1 citations · 1 across the 2 of their papers we have counts for

collaborators

5 papers

math.GR2023★ 1 cited

The Burnside problem for odd exponents

Agatha Atkarskaya, Eliyahu Rips, Katrin Tent

We show that the free Burnside groups $B (m, n)$ are infinite for $m \geq 2$ and odd $n \geq 557$ , the best currently known lower bound for the exponent. The proof uses iterated small…

math.RA2022

Small cancellation rings are non-amenable

Agatha Atkarskaya

In this paper we prove that small cancellation rings under some natural restrictions are non-amenable and contain non-commutative free associative algebra.

math.RA2020

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…

math.RA2020

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…

math.RA2018

Construction of a quotient ring of $Z_{2} F$ in which a binomial $1 + w$ 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 $Z_{2} F / I$ , where $\mathbb{Z}_2\mathc…

The Burnside problem for odd exponents

Small cancellation rings are non-amenable

Group-like small cancellation theory for rings

Small cancelation rings

Construction of a quotient ring of Z2​F in which a binomial 1+w is invertible using small cancellation methods

Construction of a quotient ring of $Z_{2} F$ in which a binomial $1 + w$ is invertible using small cancellation methods