Centralizer-dense subgroup

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WARNING: POTENTIAL TERMINOLOGICAL CONFUSION: Please don't confuse this with conjugate-dense subgroup

Definition

A subgroup of a group is termed centralizer-dense or c-dense if it satisfies the following equivalent conditions:

• Its centralizer in the whole group equals the center of the group.
• Its bicentralizer in the whole group equals the whole group.

Relation with other properties

Stronger properties

• Centralizer-free subgroup