Semihomomorphism of groups

Definition

Let $G$ and $H$ be groups. A semihomomorphism from $G$ to $H$ is a map $f:G\to H$ that satisfies, for all $a,b\in G$:

$f(aba)=f(a)f(b)f(a)$

Related notions

Stronger notions

• Antihomomorphism of groups
• Homomorphism of groups

Weaker notions

• 1-homomorphism of groups