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A note on a theorem of May concerning commutative group algebras. (English) Zbl 0704.20007

Abstract of the authors: 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 case when G itself has cardinality not exceeding \(\aleph_ 1\) and length not exceeding \(\omega_ 1\).
Reviewer: S.V.Mihovski

MSC:

20C07 Group rings of infinite groups and their modules (group-theoretic aspects)
20K10 Torsion groups, primary groups and generalized primary groups
16U60 Units, groups of units (associative rings and algebras)
16S34 Group rings
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[1] László Fuchs, Infinite abelian groups. Vol. II, Academic Press, New York-London, 1973. Pure and Applied Mathematics. Vol. 36-II. · Zbl 0257.20035
[2] Paul Hill, Isotype subgroups of totally projective groups, Abelian group theory (Oberwolfach, 1981) Lecture Notes in Math., vol. 874, Springer, Berlin-New York, 1981, pp. 305 – 321. · Zbl 0466.20028
[3] Warren May, Unit groups and isomorphism theorems for commutative group algebras, Group and semigroup rings (Johannesburg, 1985) North-Holland Math. Stud., vol. 126, North-Holland, Amsterdam, 1986, pp. 163 – 178.
[4] -, 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.
[5] Warren May, Modular group algebras of simply presented abelian groups, Proc. Amer. Math. Soc. 104 (1988), no. 2, 403 – 409. · Zbl 0691.20008
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