The relation and second homotopy modules of free Burnside groups of large even exponents

S. V. Ivanov

doi:10.1515/jgth.2000.025

The relation and second homotopy modules of free Burnside groups of large even exponents

S. V. Ivanov

Mathematics

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Abstract

A description in terms of generators and relations of the relation module of the free m-generator Burnside group B(m, n) of exponent n ≥ 2⁴⁸ divisible by 2⁹ is given and generators of the second homotopy module of a standard presentation of B(m, n) are found. This description and the generators of π₂ appear more complicated than analogous known results for free Burnside groups of odd exponent n ≫ 1.

Original language	English (US)
Pages (from-to)	323-328
Number of pages	6
Journal	Journal of Group Theory
Volume	3
Issue number	3
DOIs	https://doi.org/10.1515/jgth.2000.025
State	Published - 2000

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Algebra and Number Theory

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abstract = "A description in terms of generators and relations of the relation module of the free m-generator Burnside group B(m, n) of exponent n ≥ 248 divisible by 29 is given and generators of the second homotopy module of a standard presentation of B(m, n) are found. This description and the generators of π2 appear more complicated than analogous known results for free Burnside groups of odd exponent n ≫ 1.",

author = "Ivanov, {S. V.}",

note = "Funding Information: * Supported in part by an Alfred P. Sloan Research Fellowship and NSF grants DMS 95-01056, 98-01500",

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The relation and second homotopy modules of free Burnside groups of large even exponents

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