Orbit groups
K-Theory and Homology
2020-05-18 v3 Group Theory
Abstract
In the paper "Aquino, C., Jim\'enez, R., Mijangos, M., Morales Mel\'endez, Q.: On Invariant (co)homology of a group, preprint" are introduced two groups generated by the orbits of an action of a group on another group by automorphisms. One is of group-theoretic nature and the other comes from homology of invariant group chains. In this note are given some properties of the first groups and is studied a natural homomorphism between these groups. More precisely, it is shown that this homomorphism is not injective nor surjective. A description of the kernel is given. Note: there was a previous version with an error in the construction. The error has been corrected now.
Cite
@article{arxiv.1710.01777,
title = {Orbit groups},
author = {Quitzeh Morales Meléndez},
journal= {arXiv preprint arXiv:1710.01777},
year = {2020}
}
Comments
General construction on group theory