A note on -summable groups

Author:
Paul Hill

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

MSC (1991):
Primary 20K10, 20K07

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

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 -summable abelian -group is not determined by its socle, that is, two such groups can have isometric socles without being isomorphic. It is also demonstrated that -summability plays essentially no role in regard to the question of whether or not is totally projective, where denotes the group of normalized units of the group algebra with being a perfect field of characteristic .

**[C]**D. Cutler,*Another summable -group*, Proc. Amer. Math. Soc.**26**(1970), 43-44.**[D]**P. Danchev,*Commutative Group Algebras of a -Summable Abelian Group*, Proc. Amer. Math. Soc.**125**(1997), 2559-2564. MR**97k:20011****[LM]**R. Linton and C. Megibben,*Extensions of Totally Projective Groups*, Proc. Amer. Math. Soc.**64**(1977), 35-38.**[H]**P. Hill,*A summable -group*, Proc. Amer. Math. Soc.**23**(1969), 428-430.**[HU]**P. Hill and W. Ullery,*A note on a theorem of May concerning commutative group algebras*, Proc. Amer. Math. Soc.**110**(1990), 59-63.**[M]**W. May,*Modular group algebras of simply presented abelian groups*, Proc. Amer. Math. Soc.**104**(1988), 403-409.

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Additional Information

**Paul Hill**

Affiliation:
Department of Mathematics, Auburn University, Alabama 36849

Email:
hillpad@mail.auburn.edu

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

Received by editor(s):
February 18, 1997

Communicated by:
Ken Goodearl

Article copyright:
© Copyright 1998
American Mathematical Society