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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?)

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  • [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)
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PII: S 0002-9939(1990)1039530-4
Article copyright: © Copyright 1990 American Mathematical Society