On torsion in free central extensions of some torsion-free groups

Stöhr, Ralph

doi:10.1016/0022-4049(87)90096-x

Cited by 24 publications

(30 citation statements)

References 8 publications

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“…This exact sequence is very similar to the exact sequence obtained in Section 7.1 of [12]. However, for the convenience of the reader we include full details.…”

Section: The 6-term Exact Sequencesupporting

confidence: 56%

Free Centre-by-Metabelian Lie Rings

Mansuroğlu¹,

Stöhr²

2013

The Quarterly Journal of Mathematics

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Abstract. We study the free centre-by-metabelian Lie ring, that is, the free Lie ring with the property that the second derived ideal is contained in the centre. We exhibit explicit generating sets for the homogeneous and fine homogeneous components of the second derived ideal. Each of these components is a direct sum of a free abelian group and a (possibly trivial) elementary abelian 2-group. Our generating sets are such that some of their elements generate the torsion subgroup while the remaining ones freely generate a free abelian group. A key ingredient of our approach is the determination of the dimensions of the corresponding homogeneous and fine homogeneous components of the free centre-by-metabelian Lie algebra over fields of characteristic other than 2. For that we exploit a 6-term exact sequence of modules over a polynomial ring that is originally defined over the integers, but turns into a sequence whose terms are projective modules after tensoring with a suitable field. Our results correct a partly erroneous theorem in the literature.

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“…This exact sequence is very similar to the exact sequence obtained in Section 7.1 of [12]. However, for the convenience of the reader we include full details.…”

Section: The 6-term Exact Sequencesupporting

confidence: 56%

Free Centre-by-Metabelian Lie Rings

Mansuroğlu¹,

Stöhr²

2013

The Quarterly Journal of Mathematics

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“…In the most prominent special case, the result in question states that the free centre-by-nilpotent-by abelian groups F /[γ c (F ), F ] are torsion-free for c = 6. This is in startling contrast to the cases where c is a prime or c = 4, when for sufficiently large ranks these relatively free groups do contain elements of finite order: see [1,[7][8][9]. The present paper was motivated by these applications to abstract group theory, and indeed, our Corollary can be used to extend the results of [5] to other values of c. This will be carried out in a subsequent paper.…”

Section: Introductionmentioning

confidence: 79%

Lie powers of relation modules for groups

Kovács

Stöhr

2011

Journal of Algebra

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Motivated by applications to abstract group theory, we study Lie powers of relation modules. The relation module associated to a free presentation G = F /N of a group G is the abelianization N ab = N/ [N, N] of N, with G-action given by conjugation in F . The degree n Lie power is the homogeneous component of degree n in the free Lie ring on N ab (equivalently, it is the relevant quotient of the lower central series of N). We show that after reduction modulo a prime p this becomes a projective G-module, provided n > 1 and n is not divisible by p.Crown

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“…This was proved in [12] for the case where c is a prime, and in [13] for c = 4. A partial result for the case c = 2 was earlier established by Kuz min [10].…”

Section: Introductionmentioning

confidence: 90%