Paranormal Subgroup

In symbols,

H

is paranormal in

G

if given any

g

G

, the subgroup

K

generated by

H

and

H^g

is also equal to

H^K

. 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:

Every Pronormal Subgroup , and hence, every Normal Subgroup and every Abnormal Subgroup , is paranormal.

Every paranormal subgroup is a Polynormal Subgroup .

In finite solvable groups, every polynormal subgroup is paranormal.

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	CATEGORIES ABOUT PARANORMAL SUBGROUP

	subgroup properties

Information About

Paranormal Subgroup