Frattini-in-center group

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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A Frattini-in-center group is a group satisfying the following equivalent conditions:

Relation with other properties

Stronger properties

Weaker properties


A group of prime power order is Frattini-in-center if and only if it satisfies the following equivalent conditions:

  • It is a critical subgroup of itself.
  • It can be realized as a critical subgroup of some group of prime power order.