Finite p-group that is not characteristic in any finite p-group properly containing it
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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The existence of such groups, along with some examples and important facts, was established in a paper by Bettina Wilkens.
Suppose is a prime number and is a finite -group, i.e., a group of prime power order where the underlying prime is . We say that is a finite p-group that is not characteristic in any finite p-group properly containing it if, for any finite -group containing , is not a characteristic subgroup (i.e., characteristic subgroup of group of prime power order) of .
If and satisfies this property, and is proper in , then is not a p-finite-potentially characteristic subgroup of .