Every finite p-group is a subgroup of a finite p-group that is not characteristic in any finite p-group properly containing it

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History

This result was proved in a paper by Bettina Wilkens in 2008.

Statement

Suppose p is a prime number and P is a finite p-group, i.e., a group of prime power order. Then, there exists a finite p-group Q containing P such that for any finite p-group R properly containing Q, Q is not a characteristic subgroup of R. In other words, Q is a Finite p-group that is not characteristic in any finite p-group properly containing it (?).

Related facts

References

Journal references