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A NEW CHARACTERISATION OF m-TAME GROUPS OVER FINITELY GENERATED ABELIAN GROUPS

Published online by Cambridge University Press:  01 December 1999

DESSISLAVA H. KOCHLOUKOVA
DESSISLAVA H. KOCHLOUKOVA
Affiliation:
DPMMS, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB; [email protected]
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Abstract

It is shown that, if Q is a finitely generated abelian group, a finitely generated Q-group A is m-tame if and only if the mth tensor power of the augmentation ideal of ℤA is finitely generated over Am [rtimes ] Q, where Q acts diagonally on both Am and the tensor power. It is proved that quotients of metabelian groups of type FP3 are again of type FP3, and a necessary condition is found for a split extension of abelian-by-(nilpotent of class two) groups to be of type FP2. A conjecture is formulated that generalises the FPm-Conjecture for metabelian groups, and it is shown that one of the implications holds in the prime characteristic case.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 60 , Issue 3 , December 1999 , pp. 802 - 816
Copyright
The London Mathematical Society 1999

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