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Proceedings of the American Mathematical Society

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

 

 

On groups of finite weight


Author: P. Kutzko
Journal: Proc. Amer. Math. Soc. 55 (1976), 279-280
DOI: https://doi.org/10.1090/S0002-9939-1976-0399272-8
MathSciNet review: 0399272
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Abstract | References | Additional Information

Abstract: A subset $ S$ of a group $ G$ is said to normally generate $ G$ if the smallest normal subgroup of $ G$ which contains $ S$ is $ G$ itself. If $ \alpha $ is minimal with the property that there exist a set of cardinality $ \alpha $ which normally generates $ G$ then $ G$ is said to have weight $ \alpha $. It is shown that if $ G$ is a group of finite weight and if the lattice of those normal subgroups of $ G$ which are contained in the commutator subgroup $ G'$ of $ G$ satisfies the minimum condition then the weight of $ G$ is equal to the weight of $ G/G'$.


References [Enhancements On Off] (What's this?)

  • [1] F. González-Acuña, Homomorphs of knot groups (to appear).
  • [2] Michel A. Kervaire, On higher dimensional knots, Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton Univ. Press, Princeton, N.J., 1965, pp. 105–119. MR 0178475
  • [3] L. P. Neuwirth, Knot groups, Annals of Mathematics Studies, No. 56, Princeton University Press, Princeton, N.J., 1965. MR 0176462


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0399272-8
Article copyright: © Copyright 1976 American Mathematical Society