TY - JOUR

T1 - The Schur multiplier of F/[R, S]

AU - Abarbanel, Joseph

AU - Rosset, Shmuel

PY - 2005/6/1

Y1 - 2005/6/1

N2 - 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/γc(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.

AB - 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/γc(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.

UR - http://www.scopus.com/inward/record.url?scp=16844380316&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2004.11.011

DO - 10.1016/j.jpaa.2004.11.011

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AN - SCOPUS:16844380316

SN - 0022-4049

VL - 198

SP - 1

EP - 8

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 1-3

ER -