A note on 𝜎-summable groups

Hill, Paul

doi:10.1090/S0002-9939-98-04675-9

A note on $\sigma$-summable groups
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by Paul Hill

Proc. Amer. Math. Soc. 126 (1998), 3133-3135

DOI: https://doi.org/10.1090/S0002-9939-98-04675-9

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Abstract:

We answer questions raised by P. Danchev in a recent paper in these Proceedings. It is shown that a $\sigma$-summable abelian $p$-group is not determined by its socle, that is, two such groups can have isometric socles without being isomorphic. It is also demonstrated that $\sigma$-summability plays essentially no role in regard to the question of whether or not $V(G)/G$ is totally projective, where $V(G)$ denotes the group of normalized units of the group algebra $F(G)$ with $F$ being a perfect field of characteristic $p$.

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