Eventually isomorphic APSes of groups

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this: (facts closely related to Eventually isomorphic APSes of groups, all facts related to Eventually isomorphic APSes of groups) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
Learn more about terminology local to the wiki | view a complete list of such terminology

Definition

Let $(G,\mathrm{\Phi })$ and $(H,\mathrm{\Psi })$ be two APSes of groups. We say that $G$ and $H$ are eventually isomorphic if there exists a natural number $n_0$ and isomorphisms $G_n\to H_n$ for all $n\ge n_0$ that are compatible with the concatenation maps $\mathrm{\Phi }<math>and<math>\mathrm{\Psi }$.