The third partial cohomology group and existence of extensions of semilattices of groups by groups
arXiv:1909.00650
Abstract
We introduce the concept of a partial abstract kernel associated to a group G and a semilattice of groups A and relate the partial cohomology group H^3(G,C(A)) with the obstructions to the existence of admissible extensions of A by G which realize the given abstract kernel. We also show that if such extensions exist then they are classified by H^2(G,C(A)).
We thank the anonymous referee for the careful reading of our paper and remarks that helped us to correct several misprints and improve the proof of Lemma 2.19