Elementary abelian-to-2-subnormal replacement theorem

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This article defines a replacement theorem
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Statement

Hands-on statement

Suppose P is a Group of prime power order (?), say p^r, where p \ge 5. Let A be an elementary abelian subgroup of P.

Then, there exists an elementary abelian subgroup A^* of P such that:

Statement in terms of weak 2-subnormal replacement condition

For p at least 5 and any nonnegative integer k, the singleton set comprising the elementary abelian subgroup of order p^k is a collection of subgroups satisfying a weak 2-subnormal replacement condition.

References