= Freiman 2-isomorphism
{c}
{title2=$a_1+a_2=a_3+a_4\iff\phi(a_1)+\phi(a_2)=\phi(a_3)+\phi(a_4)$}
= Freiman isomorphism
{c}
{synonym}
= Freiman 2-isomorphic
{c}
{synonym}
A <Freiman 2-isomorphism> is a <bijection> between subsets of <abelian groups> preserving additive quadruple relations in both directions. It need not extend to an ambient group homomorphism. Multiplication by a nonzero <scalar> in a <finite field> and <translation> are examples; reduction of an <integer> set modulo a prime is an example only when it creates no new additive relations.
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