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


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
Full Text: DOI


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.