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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A note on $\sigma$-summable groups

Author: Paul Hill
Journal: Proc. Amer. Math. Soc. 126 (1998), 3133-3135
MSC (1991): Primary 20K10, 20K07
MathSciNet review: 1476137
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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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Paul Hill
Affiliation: Department of Mathematics, Auburn University, Alabama 36849

Received by editor(s): February 18, 1997
Communicated by: Ken Goodearl
Article copyright: © Copyright 1998 American Mathematical Society