@article{a9cc259043f94120bf9e5e3d17bf37ca,
title = "The third partial cohomology group and existence of extensions of semilattices of groups by groups",
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 H3 (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 H2 (G, C (A)). ",
keywords = "extension, inverse semigroup, obstruction, partial cohomology, Partial group action",
author = "Mikhailo Dokuchaev and Mykola Khrypchenko and Mayumi Makuta",
note = "info:eu-repo/grantAgreement/FCT/3599-PPCDT/PTDC%2FMAT-PUR%2F31174%2F2017/PT# The first author was partially supported by Conselho Nacional de Desenvolvimento Cientifico e Tecnologico - CNPq of Brazil (Proc. 307873/2017-0) and Fundacao de Amparo a Pesquisa do Estado de Sao Paulo - FAPESP of Brazil (Proc. 2015/09162-9). The second author was partially supported by CNPq of Brazil (Proc. 404649/2018-1). The third author was financed by Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior - Brasil (CAPES) - Finance Code 001.",
year = "2020",
month = sep,
day = "1",
doi = "10.1515/forum-2019-0281",
language = "English",
volume = "32",
pages = "1297--1313",
journal = "Forum mathematicum",
issn = "0933-7741",
publisher = "Walter de Gruyter GmbH",
number = "5",
}