Elementary 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.
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This is part of an as yet unpublished result of George Glauberman.
Suppose is a prime greater than (in other words, ). Suppose . Then, there exists a finite -group that contains an elementary abelian subgroup of order but no elementary abelian normal subgroup of order .