# Normal submonoid

From Groupprops

ANALOGY: This is an analogue in monoid of a property encountered in group. Specifically, it is a submonoid property analogous to the subgroup property: normal subgroup

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## Definition

A submonoid of a monoid is said to be **normal** if .

## Analogy

The notion of normal submonoid is the generalization to monoids of the notion of normality for subgroups. Recall that a subgroup of a group is said to be normal if .