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单词 SubnormalSubgroup
释义

subnormal subgroup


Let G be a group, and H a subgroupMathworldPlanetmathPlanetmath of G.Then H is a subnormal subgroupMathworldPlanetmath of Gif there is a natural numberMathworldPlanetmath n and subgroups H0,,Hn of Gsuch that

H=H0H1Hn=G,

where Hi is a normal subgroupMathworldPlanetmath of Hi+1 for i=0,,n-1.

Subnormality is a ,as normality of subgroups is not transitive.

We may write HsnG or HG or HG to indicate that H is a subnormal subgroup of G.

In a nilpotent groupMathworldPlanetmath, all subgroups are subnormal.

Subnormal subgroups are ascendant and descendantPlanetmathPlanetmath.

Titlesubnormal subgroup
Canonical nameSubnormalSubgroup
Date of creation2013-03-22 13:16:27
Last modified on2013-03-22 13:16:27
Owneryark (2760)
Last modified byyark (2760)
Numerical id21
Authoryark (2760)
Entry typeDefinition
Classificationmsc 20D35
Classificationmsc 20E15
Synonymsubinvariant subgroup
Synonymattainable subgroup
Related topicSubnormalSeries
Related topicClassificationOfFiniteNilpotentGroups
Related topicNormalSubgroup
Related topicCharacteristicSubgroup
Related topicFullyInvariantSubgroup
Definessubnormal
Definessubnormality
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更新时间:2025/5/4 9:48:53