Special group

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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


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

Relation with other properties

Stronger properties

Weaker properties