Abelian-to-normal replacement fails for half of prime plus nine for prime greater than five
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This result is part of an as yet unpublished paper by George Glauberman.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 is a prime number greater than (in other words, ). Suppose . Then, there exists a finite -group having an abelian subgroup of order but no abelian normal subgroup of order .
- Elementary abelian-to-normal replacement fails for half of prime plus nine for prime greater than five