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Dessislava H. Kochloukova

Modules of type FP₂ over the integral group algebra of a metabelian group

We establish a sufficient condition for some modules M over the group algebra ?[G ] to be of homological type FP₂, where G is a finitely generated split extension of abelian groups. This generalizes a result of Bieri and Strebel [R. Bieri and R. Strebel. Valuations and finitely presented metabelian groups. Proc. London Math. Soc. (3) 41 (1980), 439–464] when M is the trivial module ? and it establishes a special case of [D. H. Kochloukova. A new characterisation of m -tame groups over finitely generated abelian groups. J. London Math. Soc. (2) 60 (1999), 802–816, Conjecture K. S. Brown. Cohomology of groups (Springer-Verlag, 1982)].

Journal of Group Theory, Walter de Gruyter

Print ISSN: 1433-5883
Volume: 8, 09/2005
Seiten: 645 - 682

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