The Schur multiplier of F / [ R , S ]

It is known that if F is a free group and R is a normal subgroup such that F / R is an infinite group, then the Schur multiplier of F / γ c ( R ) is not finitely generated for all c > 1 . It is an interesting question, if R , S are two normal subgroups of the free group F, when F / [ R , S ] is f...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2005-06, Vol.198 (1), p.1-8
Main Authors: Abarbanel, Joseph, Rosset, Shmuel
Format: Article
Language:English
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Summary:It is known that if F is a free group and R is a normal subgroup such that F / R is an infinite group, then the Schur multiplier of F / γ c ( R ) is not finitely generated for all c > 1 . It is an interesting question, if R , S are two normal subgroups of the free group F, when F / [ R , S ] is finitely presented, and when is its Schur multiplier finitely generated. We show for most cases (including the cases already known) that if F / RS is infinite then the Schur multiplier of F / [ R , S ] is not finitely generated. We believe this is true in general. On the other hand if R , S are normally finitely generated and RS is of finite index, then F / [ R , S ] is finitely presented.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2004.11.011