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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive

Izv. RAN. Ser. Mat., 2025 Volume 89, Issue 4, Pages 111–218 (Mi im9475)

A sample iterated small cancellation theory for groups of Burnside type

I. G. Lysenok

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

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 $n$.

Keywords: periodic group, Burnside problem, small cancellation theory.

UDC: 512.54

MSC: Primary 20F05; Secondary 20F50, 20F06

Received: 10.03.2023

Language: English

DOI: 10.4213/im9475


 English version:
Izvestiya: Mathematics, 2025, 89:4, 758–861

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© Steklov Math. Inst. of RAS, 2025