Continuous Cohomology of Permutation Groups on Profinite Modules

ABSTRACT

Model theorists have made use of low-dimensional continuous cohomology of infinite permutation groups on profinite modules, see Ahlbrandt and Ziegler (1991), Evans (1997b), Evans et al. (1997), and Hodges and Pillay (1994), for example. We expand the module category in order to widen the cohomological toolkit. For an important class of groups we use these tools to establish criteria for finiteness of cohomology.

Keywords:

• Cohomology
• Permutation groups
• Profinite modules

Mathematics Subject Classification (2000):

• 20B27
• 22E41
• 03C99

Notes

Communicated by H. Macpherson.