Our aim is to transfer many of the foundational results from the modular representation theory of finite groups to the wider context of profinite groups. We are thus interested in profinite modules over the completed group algebra k[[G]] of a profinite group G, where kc is a finite field of characteristic p. Our approach is as follows. We define the concept of relative projectivity for a profinite module over k[[G]] and prove a characterization analogous to the finite case with additions of interest to the pro and sources for indecomposable finitely generated k[[G]]-modules, extending several results known to hold in the finite case. For sources this requires additional assumptions. We prove a direct analogue of Green's Indecomposability Theorem for finitely generated modules over a virtually pro-p group, as well as a lesser known variant due to M.E. Harris. We give a version of the Green Correspondence for finitely generated modules over virtually pro-p groups.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:496232 |
| Date | January 2009 |
| Creators | MacQuarrie, John William |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
Page generated in 0.0016 seconds