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单词 NormalClosure1
释义

normal closure


Let S be a subset of a group G.The normal closurePlanetmathPlanetmath of S in G is the intersection of all normal subgroupsMathworldPlanetmath of G that contain S, that is

SNGN.

The normal closure of S is the smallest normal subgroup of G that contains S, and so is also called the normal subgroup generated by S.

It is not difficult to show that the normal closure of S is the subgroupMathworldPlanetmathPlanetmath generated by all the conjugates of elements of S.

The normal closure of S in G is variously denoted bySG or SG or SG.

If H is a subgroup of G,and H is of finite index in its normal closure,then H is said to be nearly normal.

Titlenormal closure
Canonical nameNormalClosure1
Date of creation2013-03-22 14:41:50
Last modified on2013-03-22 14:41:50
Owneryark (2760)
Last modified byyark (2760)
Numerical id9
Authoryark (2760)
Entry typeDefinition
Classificationmsc 20A05
Synonymnormal subgroup generated by
Synonymconjugate closure
Synonymsmallest normal subgroup containing
Related topicNormalizerMathworldPlanetmath
Related topicCoreOfASubgroup
Definesnearly normal
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更新时间:2025/5/4 11:48:23