Neha Patil (Editor)

Centrally closed subgroup

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In mathematics, in the realm of group theory, a subgroup of a group is said to be centrally closed if the centralizer of any nonidentity element of the subgroup lies inside the subgroup.

Some facts about centrally closed subgroups:

  • Every malnormal subgroup is centrally closed.
  • Every Frobenius kernel is centrally closed.
  • SA subgroups are precisely the centrally closed Abelian subgroups.
  • The trivial subgroup and the whole group are centrally closed.

    • References

    Centrally closed subgroup Wikipedia
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