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 ) ) {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 ) ) {H^{2}(G,C(A))} .

中文翻译：

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第三部分上同调群及群的半格扩展的存在性

摘要 我们引入了与群 G 和群 A 的半格相关联的部分抽象核的概念，并将部分上同调群 H 3 ⁢ ( G , C ⁢ ( A ) ) {H^{3}(G,C( A))} 与实现给定抽象内核的 G 的可容许扩展的存在的障碍。我们还表明，如果存在这样的扩展，则它们按 H 2 ⁢ ( G , C ⁢ ( A ) ) {H^{2}(G,C(A))} 分类。