Minimal characteristic implies central in nilpotent

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This article gives the statement and possibly, proof, of an implication relation between two subgroup properties, when the big group is a [[{{{group property}}}]]. That is, it states that in a , every subgroup satisfying the first subgroup property must also satisfy the second subgroup property . In other words, every is a .
[[:Category:Subgroup property implications in {{{group property}}}s|View all subgroup property implications in {{{group property}}}s]] | [[:Category:Subgroup property non-implications in {{{group property}}}s|View all subgroup property non-implications in {{{group property}}}s]] | View all subgroup property implications | View all subgroup property non-implications
[[Category:Subgroup property implications in {{{group property}}}s]]


In a nilpotent group, any Minimal characteristic subgroup (?) is central: it is contained in the center of the whole group.

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