Alternating forms and one-relator groups
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- by Jack Sonn
- Proc. Amer. Math. Soc. 46 (1974), 15-20
- DOI: https://doi.org/10.1090/S0002-9939-1974-0367070-5
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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.References
- E. Artin, Geometric algebra, Interscience Publishers, Inc., New York-London, 1957. MR 0082463
- Jack Shapiro and Jack Sonn, Free factor groups of one-relator groups, Duke Math. J. 41 (1974), 83–88. MR 347989
- Arthur Steinberg, On free nilpotent quotient groups, Math. Z. 85 (1964), 185–196. MR 191949, DOI 10.1007/BF01110375 J.-P. Serre, Cohomologie galoisienne, 2nd ed., Lecture Notes in Math., vol. 5, Springer-Verlag, Berlin and New York, 1964. MR 31 #4785.
- John P. Labute, Classification of Demushkin groups, Canadian J. Math. 19 (1967), 106–132. MR 210788, DOI 10.4153/CJM-1967-007-8
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- 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