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arXiv · 1909.00650

The third partial cohomology group and existence of extensions of semilattices of groups by groups

Mikhailo Dokuchaev·Mykola Khrypchenko·Mayumi Makuta
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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)).

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Mikhailo Dokuchaev, Mykola Khrypchenko, Mayumi Makuta. 2019-09-02. The third partial cohomology group and existence of extensions of semilattices of groups by groups. https://arxiv.org/abs/1909.00650

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