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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Alternating forms and one-relator groups


Author: Jack Sonn
Journal: Proc. Amer. Math. Soc. 46 (1974), 15-20
MSC: Primary 20F05; Secondary 20J05
DOI: https://doi.org/10.1090/S0002-9939-1974-0367070-5
MathSciNet review: 0367070
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Abstract: This paper considers epimorphisms of finitely generated one-relator groups $ G = F/R,F$ free, $ R \subseteq {F^p}[F,F]$ for some rational prime $ p$. The main result is a lower bound for the difference rank $ G$-rank $ G'$ when $ G'$ is a one-relator group homomorphic to $ G$. This generalizes a known result for the case $ G'$ a free group.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0367070-5
Keywords: Alternating forms, one-relator groups, cohomology, factor groups, nilpotent groups, rank
Article copyright: © Copyright 1974 American Mathematical Society