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The modular group algebra problem for metacyclic $p$-groups

Author(s): Robert Sandling
Journal: Proc. Amer. Math. Soc. 124 (1996), 1347-1350.
MSC (1991): Primary 20C05; Secondary 16S34, 16U60, 20C20, 20D15, 20F05
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Abstract: It is shown that the isomorphism type of a metacyclic $p$-group is determined by its group algebra over the field $F$ of $p$ elements. This completes work of Baginski. It is also shown that, if a $p$-group $G$ has a cyclic commutator subgroup $G'$, then the order of the largest cyclic subgroup containing $G'$ is determined by $FG$.

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Additional Information:

Robert Sandling
Affiliation: Department of Mathematics, The University, Manchester M13 9PL, England
Email: rsandling@manchester.ac.uk

DOI: 10.1090/S0002-9939-96-03518-6
PII: S 0002-9939(96)03518-6
Keywords: Modular group algebra, $p$-group, isomorphism problem, metacyclic
Received by editor(s): July 11, 1994
Communicated by: Ronald M. Solomon
Copyright of article: Copyright 1996, American Mathematical Society

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