Normal closure of finite subset: Difference between revisions
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==Definition== | ==Definition== | ||
A [[subgroup]] of a [[group]] is termed a '''normal closure of finite subset''' if there is a finite subset of that subgroup such that the [[defining ingredient::normal | A [[subgroup]] of a [[group]] is termed a '''normal closure of finite subset''' if there is a finite subset of that subgroup such that the [[defining ingredient::normal subgroup generated by a subset|normal subgroup generated]] by that finite subset in the ''whole group'' is the subgroup. In other words, the subgroup arises as the [[defining ingredient::normal closure]] in the whole group of a [[defining ingredient::finitely generated group|finitely generated subgroup]]. | ||
==Relation with other properties== | ==Relation with other properties== | ||
Latest revision as of 20:41, 27 April 2010
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
Definition
A subgroup of a group is termed a normal closure of finite subset if there is a finite subset of that subgroup such that the normal subgroup generated by that finite subset in the whole group is the subgroup. In other words, the subgroup arises as the normal closure in the whole group of a finitely generated subgroup.