Center is marginal of finite type

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This article gives the statement, and possibly proof, of the fact that for any group, the subgroup obtained by applying a given subgroup-defining function (i.e., center) always satisfies a particular subgroup property (i.e., marginal subgroup of finite type)}
View subgroup property satisfactions for subgroup-defining functions  View subgroup property dissatisfactions for subgroup-defining functions

Statement

The center of a group is a marginal subgroup of finite type, and hence a marginal subgroup. More specifically, it is the marginal subgroup corresponding to the commutator word .

Related facts

Corollaries

Property Statement about marginal subgroups Corresponding statement about center
bound-word subgroup marginal implies bound-word center is bound-word
strictly characteristic subgroup marginal implies strictly characteristic center is strictly characteristic
finite direct power-closed characteristic subgroup marginal implies direct power-closed characteristic center is direct power-closed characteristic
characteristic subgroup marginal implies characteristic center is characteristic