Paranormal subgroup

In mathematics, in the field of group theory, a paranormal subgroup is a subgroup such that the subgroup generated by it and any conjugate of it, is also generated by it and a conjugate of it within that subgroup.

In symbols, is paranormal in if given any in , the subgroup generated by and is also equal to . Equivalently, a subgroup is paranormal if its weak closure and normal closure coincide in all intermediate subgroups.

Here are some facts relating paranormality to other subgroup properties:

Kantor, William M.; Martino, Lino Di (12 January 1995). Groups of Lie Type and Their Geometries. Cambridge University Press. pp. 257–259. ISBN 9780521467902.

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