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

Autor(es)

Dokuchaev, Mikhailo ^[1] ; Khrypchenko, Mykola ^{[2, 3]} ; Makuta, Mayumi ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

^[2] Univ Fed Santa Catarina, Dept Matemat, Campus Reitor Joao David Ferreira Lima, BR-88040900 Florianopolis, SC - Brazil

^[3] Univ Nova Lisboa, Ctr Matemat & Aplicacoes, Fac Ciencias & Tecnol, P-2829516 Caparica - Portugal

• Tipo de documento: Artigo Científico
• Fonte: FORUM MATHEMATICUM; v. 32, n. 5, p. 1297-1313, SEP 2020.
• Citações Web of Science: 0

Resumo

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)). (AU)

• Processo FAPESP: 15/09162-9 - Álgebra não comutativa e aplicações
• Beneficiário: Francisco Cesar Polcino Milies
• Modalidade de apoio: Auxílio à Pesquisa - Temático