Binate group

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

Definition with symbols

A group G is termed a binate group if for every finitely generated subgroup H of G there is a homomorphism \varphi_H: H \to G and an element u_H \in G such that for all h \in H, we have:

h = [u_H, \varphi_H(h)].

Relation with other properties

Weaker properties