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

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)).

preprint2020arXivOpen access
Mikhailo DokuchaevMykola KhrypchenkoMayumi Makuta
math.GR
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Mikhailo DokuchaevMykola KhrypchenkoMayumi Makuta

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