Difference between revisions of "Descendant subgroup"
From Encyclopedia of Mathematics
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{{MSC|20F14}} | {{MSC|20F14}} | ||
| − | A [[subgroup]] of a [[ | + | A [[subgroup]] of a [[group]] for which there is a descending series starting from the subgroup and ending at the group, such that every term in the series is a [[normal subgroup]] of its predecessor. The series may be an infinite [[subgroup system]]. If the series is finite, then the subgroup is [[subnormal subgroup|subnormal]]. |
==References== | ==References== | ||
* Martyn R. Dixon, "Sylow Theory, Formations, and Fitting Classes", in ''Locally Finite Groups'' (World Scientific, 1994) ISBN 9810217951, p.6 | * Martyn R. Dixon, "Sylow Theory, Formations, and Fitting Classes", in ''Locally Finite Groups'' (World Scientific, 1994) ISBN 9810217951, p.6 | ||
Revision as of 18:48, 7 September 2013
2020 Mathematics Subject Classification: Primary: 20F14 [MSN][ZBL]
A subgroup of a group for which there is a descending series starting from the subgroup and ending at the group, such that every term in the series is a normal subgroup of its predecessor. The series may be an infinite subgroup system. If the series is finite, then the subgroup is subnormal.
References
- Martyn R. Dixon, "Sylow Theory, Formations, and Fitting Classes", in Locally Finite Groups (World Scientific, 1994) ISBN 9810217951, p.6
How to Cite This Entry:
Descendant subgroup. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Descendant_subgroup&oldid=30412
Descendant subgroup. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Descendant_subgroup&oldid=30412