# Orbital maximax is bounded below by constant fraction of number of ordered pairs of distinct elements for groups of fixed prime power order

From Groupprops

## Contents

## Statement

Suppose is a (fixed) prime number. Consider the Orbital maximax problem (?) for finite -groups acting on a set of size : we want to find the maximum possible size of the largest orbital under the action of a finite -group on .

The claim is that there is a constant (depending on , and in fact of the order of ), such that for any , there is a group action such that size of the largest orbital is .

## Related facts

### Related facts about orbital maximax

Type of group | Result |
---|---|

abelian group | Orbital maximax equals size of set for abelian groups |

nilpotent group | (this page) |