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Difference between revisions of "Descendant subgroup"

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(Start article: Descendant subgroup)
 
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{{MSC|20F14}}
 
{{MSC|20F14}}
  
A  [[subgroup]] of a [[group (mathematics)|group]] for which there is an  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 infinite. If the series is finite, then the subgroup is [[subnormal subgroup|subnormal]].  
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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=30410