The third partial cohomology group and existence of extensions of semilattices of groups by groups-Reference-Cited by-同舟云学术

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

Published:2020-09-01 Issue:5 Volume:32 Page:1297-1313
ISSN:1435-5337
Container-title:Forum Mathematicum
language:
Short-container-title:

Author:

Dokuchaev Mikhailo¹,Khrypchenko Mykola²,Makuta Mayumi¹

Affiliation:

1. Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, São Paulo, SP, CEP: 05508–090, Brazil

2. Departamento de Matemática, Universidade Federal de Santa Catarina, Campus Reitor João David Ferreira Lima, Florianópolis, SC, CEP: 88040–900, Brazil; and Centro de Matemática e Aplicações, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2829–516 Caparica, Portugal

Abstract

AbstractWe 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))}

Funder

Fundaçǎo de Amparo à Pesquisa do Estado de Sǎo Paulo

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Coordenaçǎo de Aperfeiçoamento de Pessoal de Nìvel Superior

Fundaçǎo para a Ciência e a Tecnologia

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2019-0281/pdf

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