PlanetMath: abnormal subgroup

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abnormal subgroup

(Definition)

A subgroup of a group is called an abnormal subgroup if $x\in{\left\langle H,xHx^{-1}\right\rangle}$ for all $x\in G$ .

Some facts about abnormal subgroups:

"abnormal subgroup" is owned by yark.

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Also defines:

abnormal, abnormality

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Cross-references: pronormal subgroup, normalizer, maximal subgroups, self-normalizing, pronormal, group, subgroup
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This is version 1 of abnormal subgroup, born on 2006-12-18.
Object id is 8635, canonical name is AbnormalSubgroup.
Accessed 1061 times total.

Classification:

20E99 (Group theory and generalizations :: Structure and classification of infinite or finite groups :: Miscellaneous)

Pending Errata and Addenda

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