Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772888 | Journal of Pure and Applied Algebra | 2017 | 13 Pages |
Abstract
The article is devoted to extending the notions of the c-nilpotent multiplier and the c-stem cover of a group to the crossed modules context. We give a five-term exact sequence in the c-nilpotent multiplier associated with an extension of crossed modules from which we deduce a generalization version of the Basic Theorem of Grandjean and Ladra (1998) [9] relating nilpotent crossed modules to their second homologies. We also study c-stem extensions and c-covers of crossed modules and prove that any c-stem extension of a perfect crossed module is a homomorphic image of its c-stem cover. Finally, we show that the c-nilpotent multipliers of a perfect crossed module are isomorphic to each other. This generalizes the work of Burns and Ellis (1997) [5] in group theory.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ali Reza Salemkar, Sajedeh Talebtash, Zahra Riyahi,