Abnormal subgroup
id:
abnormal-subgroup-246-7550131
title:
Abnormal subgroup
text:
In mathematics, specifically group theory, an abnormal subgroup is a subgroup H of a group G such that for all x in G, x lies in the subgroup generated by H and H x, where H x denotes the conjugate subgroup xHx−1. Here are some facts relating abnormality to other subgroup properties: Every abnormal subgroup is a self-normalizing subgroup, as well as a contranormal subgroup.
The only normal subgroup that is also abnormal is the whole group.
Every abnormal subgroup is a weakly abnormal subgroup, a
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wiki
category slug:
encyclopedia
description:
original url:
https://en.wikipedia.org/wiki/Abnormal_subgroup
date created:
date modified:
2023-08-12T23:53:11Z
main entity:
{"identifier":"Q4668179","url":"https://www.wikidata.org/entity/Q4668179"}
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13
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