Homology, Homotopy and Applications

Volume 2 (2000)

Number 1

More about homological properties of precrossed modules

Pages: 105 – 114

DOI: https://dx.doi.org/10.4310/HHA.2000.v2.n1.a7

Authors

Nick Inassaridze (A. Razmadze Mathematical Institute, Georgian Academy of Sciences, Tbilisi, Republic of Georgia)

Emzar Khmaladze (A. Razmadze Mathematical Institute, Georgian Academy of Sciences, Tbilisi, Republic of Georgia)

Abstract

Homology groups modulo $q$ of a precrossed $P$-module in any dimensions are defined in terms of nonabelian derived functors, where $q$ is a nonnegative integer. The Hopf formula is proved for the second homology group modulo $q$ of a precrossed $P$-module which shows that for $q=0$ our definition is a natural extension of Conduché and Ellis’ definition [CE]. Some other properties of homologies of precrossed $P$-modules are investigated.

Keywords

precrossed module, Peiffer abelianization, homology group, nonabelian derived functor

2010 Mathematics Subject Classification

18G10, 18G50, 20J05

Published 1 January 2000