P-hyperelementary 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
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Definition

A finite group is termed p-hyperelementary if it satisfies the following equivalent conditions:

  1. It is the internal semidirect product of a cyclic group of order relatively prime to p with a p-group.
  2. It is the internal semidirect product of a cyclic group and a p-group.
  3. It contains a cyclic normal p-complement.

Relation with other properties

Stronger properties