1 results
COHOMOLOGY AND PROFINITE TOPOLOGIES FOR SOLVABLE GROUPS OF FINITE RANK
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 86 / Issue 2 / October 2012
- Published online by Cambridge University Press:
- 16 February 2012, pp. 254-265
- Print publication:
- October 2012
-
- Article
-
- You have access
- Export citation
-
Assume that G is a solvable group whose elementary abelian sections are all finite. Suppose, further, that p is a prime such that G fails to contain any subgroups isomorphic to Cp∞. We show that if G is nilpotent, then the pro-p completion map
induces an isomorphism 
for any discrete 
-module M of finite p-power order. For the general case, we prove that G contains a normal subgroup N of finite index such that the map 
is an isomorphism for any discrete 
-module M of finite p-power order. Moreover, if G lacks any Cp∞-sections, the subgroup N enjoys some additional special properties with respect to its pro-p topology.
induces an isomorphism 
for any discrete 
-module 
is an isomorphism for any discrete 
-module 