Abelian-to-normal replacement fails for half of prime plus nine for prime greater than five

From Groupprops
Jump to: navigation, search
This article discusses a failure of replacement, i.e., a situation where the analogue of a valid replacement theorem fails to hold under slightly modified conditions.
View other failures of replacement | View replacement theorems


This result is part of an as yet unpublished paper by George Glauberman.


Suppose p is a prime number greater than 5 (in other words, p \ge 7). Suppose k \ge (p + 9)/2. Then, there exists a finite p-group P having an abelian subgroup of order p^k but no abelian normal subgroup of order p^k.

Related facts

Similar facts

Opposite facts