# Marginal homomorphism

From Groupprops

## Definition

Suppose is a subvariety of the variety of groups. Suppose and are groups (not necessarily in , and in fact, definitely not in the interesting cases). Suppose is a homomorphism of groups. We say that is a -**marginal homomorphism** if where and denote respectively the -marginal subgroups of and .

## Particular cases

- In case is the subvariety comprising only the trivial group, all homomorphisms are marginal homomorphisms.
- In case is the subvariety comprising all groups, all homomorphisms are marginal homomorphisms.
- In case is the subvariety comprising abelian groups only, the marginal homomorphism are precisely the central homomorphisms.