Corollary of Timmesfeld's replacement theorem for abelian subgroups

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
This article is about a maximality notion among subgroups, related to abelianness or small class, in a group of prime power order.
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Statement

Suppose is a group of prime power order. Let denote the set of abelian subgroups of maximum order in . If , and is an -invariant abelian subgroup of . Then, is an abelian subgroup of maximum order.

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References

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