Abelian-to-normal replacement theorem for prime exponent

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This article defines a replacement theorem
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Statement

Suppose P is a finite Group of prime exponent (?): group of prime power order, say p^r, and with exponent p (so every element has order p). Suppose A is an abelian subgroup of order p^n, and nilpotency class at most p + 1.

Then, there exists an Abelian normal subgroup (?) B of P such that:

Related facts

References