Free central extensions of groups and modular Lie powers of relation modules

Marianne Johnson; Ralph Stöhr

doi:10.1090/S0002-9939-2010-10409-4

Free central extensions of groups and modular Lie powers of relation modules

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Abstract

The most prominent special case of our main result is that the free centre-by-(nilpotent of class (c - 1))-by-abelian groups F/[γc(F'), F] are torsion-free whenever c is divisible by at least two distinct primes. This is in stark contrast to the case where c is a prime or c = 4, where these relatively free groups contain non-trivial elements of finite order. © 2010 American Mathematical Society.

Original language	English
Pages (from-to)	3807-3814
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	138
Issue number	11
DOIs	https://doi.org/10.1090/S0002-9939-2010-10409-4
Publication status	Published - Nov 2010

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http://www.ams.org/journals/proc/2010-138-11/S0002-9939-2010-10409-4/S0002-9939-2010-10409-4.pdf

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AB - The most prominent special case of our main result is that the free centre-by-(nilpotent of class (c - 1))-by-abelian groups F/[γc(F'), F] are torsion-free whenever c is divisible by at least two distinct primes. This is in stark contrast to the case where c is a prime or c = 4, where these relatively free groups contain non-trivial elements of finite order. © 2010 American Mathematical Society.

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DO - 10.1090/S0002-9939-2010-10409-4

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JO - Proceedings of the American Mathematical Society

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Free central extensions of groups and modular Lie powers of relation modules

Abstract

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