Gareth Wilkes
Published 2022-09-14Version 1
We construct a correspondence between the cohomology groups of a group $G$ relative to a family of subgroups $\famS$ and the classes of `relative extensions' of $G$ by abelian groups, modulo a certain equivalence relation. We establish this correspondence for both discrete and profinite group pairs. We go on to discuss the relationships of profinite group pairs of cohomological dimension one with free products and projective group pairs.
Every decidable pseudovariety of abelian groups is completely tame
Abelian groups are polynomially stable
On matchable subsets in abelian groups and their linear analogues
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