Abelian-to-normal replacement theorem for prime exponent
This article defines a replacement theorem
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Suppose is a finite Group of prime exponent (?): group of prime power order, say , and with exponent (so every element has order ). Suppose is an abelian subgroup of order , and nilpotency class at most .
Then, there exists an Abelian normal subgroup (?) of such that:
- Mann's replacement theorem for subgroups of prime exponent
- p-group is either absolutely regular or maximal class or has normal subgroup of exponent p and order p^p
- Group of exponent p and order greater than p^p is not embeddable in a maximal class group