Finite p-group that is not characteristic in any finite p-group properly containing it

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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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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

History

The existence of such groups, along with some examples and important facts, was established in a paper by Bettina Wilkens.

Definition

Suppose p is a prime number and P is a finite p-group, i.e., a group of prime power order where the underlying prime is p. We say that P is a finite p-group that is not characteristic in any finite p-group properly containing it if, for any finite p-group Q containing P, P is not a characteristic subgroup (i.e., characteristic subgroup of group of prime power order) of Q.

If P \le Q and P satisfies this property, and P is proper in Q, then P is not a p-finite-potentially characteristic subgroup of Q.

Facts

References

Journal references