abnormal subgroup

A subgroup $H$ of a group $G$ is called an abnormal subgroup if $x\in ⟨H,xH{x}^{-1}⟩$ for all $x\in G$.

Some facts about abnormal subgroups:

• Abnormal subgroups are pronormal and self-normalizing.

• Non-normal (http://planetmath.org/NormalSubgroup) maximal subgroups are abnormal.

• The normalizer of a pronormal subgroup is abnormal.

Title	abnormal subgroup
Canonical name	AbnormalSubgroup
Date of creation	2013-03-22 16:28:15
Last modified on	2013-03-22 16:28:15
Owner	yark (2760)
Last modified by	yark (2760)
Numerical id	4
Author	yark (2760)
Entry type	Definition
Classification	msc 20E99
Defines	abnormal
Defines	abnormality