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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on a theorem of May concerning commutative group algebras


Authors: Paul Hill and William Ullery
Journal: Proc. Amer. Math. Soc. 110 (1990), 59-63
MSC: Primary 20C07; Secondary 20K10
MathSciNet review: 1039530
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Abstract: Let $ G$ be a coproduct of $ p$-primary abelian groups with each factor of cardinality not exceeding $ {\aleph _1}$, and let $ F$ be a perfect field of characteristic $ p$. If $ V(G)$ is the group of normalized units of the group algebra $ F(G)$, it is shown that $ G$ is a direct factor of $ V(G)$ and that the complementary factor is simply presented. This generalizes a theorem of W. May, who proved the result in the case when $ G$ itself has cardinality not exceeding $ {\aleph _1}$ and length not exceeding $ {\omega _1}$.


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

  • [F] L. Fuchs, Infinite abelian groups, vol. II, Academic Press, New York, 1973. MR 0349869 (50:2362)
  • [H] P. Hill, Isotype subgroups of totally projective groups, Abelian Group Theory, Lecture Notes in Math., vol. 874, Springer-Verlag, Berlin, Heidelberg, and New York, 1981, pp. 305-321. MR 645937 (83e:20057)
  • [M1] W. May, Unit groups and isomorphism theorems for commutative group algebras, Groups and Semigroup Rings, North-Holland Math. Studies, no. 126, North-Holland, Amsterdam, 1986, pp. 163-178. MR 860059 (87m:16025)
  • [M2] -, The direct factor problem for modular group algebras, Representation Theory, Group Rings, and Coding Theory, Contemp. Math., vol. 93, Amer. Math. Soc., Providence, RI, 1989, pp. 303-308.
  • [M3] -, Modular group algebras of simply presented abelian groups, Proc. Amer. Math. Soc. 104 (1988), 403-409. MR 962805 (89k:20080)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1039530-4
PII: S 0002-9939(1990)1039530-4
Article copyright: © Copyright 1990 American Mathematical Society