Center of second center

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This article defines a subgroup-defining function, viz., a rule that takes a group and outputs a unique subgroup
View a complete list of subgroup-defining functions OR View a complete list of quotient-defining functions

Definition

The center of second center of a group is defined as the center of its second center.

Relation with other subgroup-defining functions

Smaller subgroup-defining functions

Subgroup-defining function Meaning
center centralizes every element of the group

Larger subgroup-defining functions

Subgroup-defining function Meaning
second center image in inner automorphism group equals center of inner automorphism group