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Abstract
The zeroeth complete cohomology of a group G with coefficients in , is known to carry much information about the group. Its computation is rather complicated. Kropholler (Citation1993b) and Benson and Kropholler (Citation1995) stated that even when G is a polycyclic by finite group, no general formula is known for
. Here we construct a projective resolution for a class of polycyclic groups and obtain information about
, which indicates that no general formula for
can be expected.
Moreover, some groups in our class are counterexamples to a conjecture of Brown, which states that the least common multiple of the orders of the finite subgroups of a group of finite virtual cohomological dimension annihilates the complete cohomology of G. The first counterexample to this conjecture was given by Adem (Citation1989) and more were obtained later by Adem and Carlson (Citation1990) and Leary (Citation1996). We obtain counterexamples that are not in those classes.
2000 Mathematics Subject Classification:
ACKNOWLEDGMENTS
The present study was funded through the program EPEAEK II in the framework of the project “Pythagoras – Support of University Research Groups” with 75% from European Social Funds and 25% from National Funds.
Notes
Communicated by T. H. Lenagan.