2 results
Profinite detection of 3-manifold decompositions
- Part of
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- Journal:
- Compositio Mathematica / Volume 155 / Issue 2 / February 2019
- Published online by Cambridge University Press:
- 07 January 2019, pp. 246-259
- Print publication:
- February 2019
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- Article
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The profinite completion of the fundamental group of a closed, orientable
$3$-manifold determines the Kneser–Milnor decomposition. If 
$M$ is irreducible, then the profinite completion determines the Jaco–Shalen–Johannson decomposition of 
$M$.
COHOMOLOGY AND PROFINITE TOPOLOGIES FOR SOLVABLE GROUPS OF FINITE RANK
- Part of
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- 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
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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 