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

Mikhailo Dokuchaev, Mykola Khrypchenko, Mayumi Makuta

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1 Citation (Scopus)

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)).

Original languageEnglish
Pages (from-to)1297-1313
Number of pages17
JournalForum mathematicum
Volume32
Issue number5
DOIs
Publication statusPublished - 1 Sep 2020

Keywords

  • extension
  • inverse semigroup
  • obstruction
  • partial cohomology
  • Partial group action

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