Every finite p-group is a subgroup of a finite p-group that is not characteristic in any finite p-group properly containing it
From Groupprops
History
This result was proved in a paper by Bettina Wilkens in 2008.
Statement
Suppose is a prime number and is a finite -group, i.e., a group of prime power order. Then, there exists a finite -group containing such that for any finite -group properly containing , is not a characteristic subgroup of . In other words, is a Finite p-group that is not characteristic in any finite p-group properly containing it (?).
Related facts
- Normal subgroups need not be finite-p-potentially characteristic subgroups.
- Normal not implies finite-pi-potentially characteristic
References
Journal references
- Finite p-groups not characteristic in any finite p-group in which they are properly contained by Bettina Wilkens, , Volume 166, Page 97 - 112(Year 2008): ^{Official copy (PDF)(gated)}^{More info}