C-closed self-centralizing subgroup
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: c-closed subgroup and self-centralizing subgroup
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- Its centralizer equals its center and it equals the centralizer of its center (all relative to the whole group).
- It is self-centralizing (i.e., it contains its own centralizer in the whole group) and also occurs as the centralizer of some subgroup of the whole group.
- It occurs as the centralizer of some Abelian subgroup of the whole group.
Definition with symbols
- and .
- and there exists a subgroup such that .
- There exists an Abelian subgroup of such that .