Special group (finite group theory)

In group theory, a discipline within abstract algebra, a special group is a finite group of prime power order that is either elementary abelian itself or of class 2 with its derived group, its center, and its Frattini subgroup all equal and elementary abelian (Gorenstein 1980, p.183). A special group of order pⁿ that has class 2 and whose derived group has order p is called an extra special group.

References

Gorenstein, D. (1980), Finite groups (2nd ed.), New York: Chelsea Publishing Co., ISBN 978-0-8284-0301-6, MR 0569209

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