# Sims-reduced generating set

From Groupprops

*This article defines a property that can be evaluated for a generating set of a permutation group: a group equipped with an embedding in a symmetric group on an ordered set*

## Definition

Let be a group acting on a set of size (equivalent is equipped with an embedding in the symmetric group on elements). A **Sims-reduced generating set** is a generating set for where for any elements , there is at most one elements of which fixes all elements less than and sends to .

Any generating set for can be trimmed down to a Sims-reduced generating set using the Sims filter.