A sample iterated small cancellation theory for groups of Burnside type

We develop yet another technique to present the free Burnside group $B(m,n)$ of odd exponent $n$ with $m\ge2$ generators as a group satisfying a certain iterated small cancellation condition. Using the approach, we provide a reasonably accessible proof that $B(m,n)$ is infinite with a moderate bound $n > 2000$ on the odd exponent $n$.

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Publication Details

Journal
Izvestiya Mathematics
Published
2025-01-01
DOI
https://doi.org/10.4213/im9475e
Primary Topic
Finite Group Theory Research
Type
article
Field-Weighted Citation Impact
0.00

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article

A sample iterated small cancellation theory for groups of Burnside type

Igor Lysenok
Izvestiya Mathematics
Finite Group Theory Research
article

A sample iterated small cancellation theory for groups of Burnside type

Igor Lysenok
article en

Abstract

We develop yet another technique to present the free Burnside group $B(m,n)$ of odd exponent $n$ with $m\ge2$ generators as a group satisfying a certain iterated small cancellation condition. Using the approach, we provide a reasonably accessible proof that $B(m,n)$ is infinite with a moderate bound $n > 2000$ on the odd exponent $n$.

Izvestiya MathematicsVol. 89(4)
Russian Academy of Sciences (RU), Steklov Mathematical Institute (RU)
Russian Science Foundation
Openalex Percentile: Top 71%
Finite Group Theory Research
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