The modular group algebra problem for metacyclic 𝑝-groups

Author:

Sandling Robert

Abstract

It is shown that the isomorphism type of a metacyclic p p -group is determined by its group algebra over the field F F of p p elements. This completes work of Bagiński. It is also shown that, if a p p -group G G has a cyclic commutator subgroup G G’ , then the order of the largest cyclic subgroup containing G G’ is determined by F G FG .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference13 articles.

1. The isomorphism question for modular group algebras of metacyclic 𝑝-groups;Bagiński, Czesław;Proc. Amer. Math. Soc.,1988

2. F. R. Beyl, The classification of metacyclic 𝑝-groups, and other applications of homological algebra to group theory, Ph. D. thesis, Cornell Univ., 1972.

3. Die Grundlehren der mathematischen Wissenschaften, Band 134;Huppert, B.,1967

4. Presentations of metacyclic groups;King, Bruce W.;Bull. Austral. Math. Soc.,1973

5. Bemerkungen über die Gruppenalgebra als symmetrische Algebra;Külshammer, Burkhard;J. Algebra,1981

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