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arxiv 2303.15997 v5 pith:DJL6GPYB submitted 2023-03-28 math.GR

The Burnside problem for odd exponents

Agatha Atkarskaya , Eliyahu Rips , Katrin Tent This is my paper
classification math.GR
keywords burnsidebestboundcancellationcertificationconceptcurrentlydepth
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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 cancellation theory where the induction is based on the nesting depth of relators. The main instrument at every step is a new concept of a certification sequence.

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Cited by 2 Pith papers

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  1. Asymptotic Burnside laws

    math.GR 2024-09 unverdicted novelty 7.0

    Finitely generated groups are built that satisfy Burnside laws with limit probability 1 (or 0, or any partial limit in [0,1]) under ball measures and random walks, resolving open questions on sensitivity to generators...

  2. From the Cherlin-Zilber Conjecture via sharply $2$-transitive groups to the Burnside problem

    math.LO 2026-06 unverdicted novelty 1.0

    A review outlining the Cherlin-Zilber Algebraicity Conjecture, the potential role of sharply 2-transitive groups as counterexamples, and connections to the Burnside problem.