# Special group

From Groupprops

The article defines a property of groups, where the definition may be in terms of a particular prime that serves as parameter

View other prime-parametrized group properties | View other group properties

## Contents

## Definition

A group of prime power order is termed **special** if its center, derived subgroup and Frattini subgroup all coincide. It turns out that in this case, the center must be an elementary abelian group.

Sometimes, the term **special** also includes the case of elementary abelian groups. Under this definition, a group is special if it is either special in the above sense *or* it is elementary abelian.

`Further information: Special implies center is elementary abelian`