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Orbit groups

In the paper "Aquino, C., Jiménez, R., Mijangos, M., Morales Meléndez, 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.

preprint2020arXivOpen access
Quitzeh Morales Meléndez
math.GRmath.KT
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Quitzeh Morales Meléndez

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