Powering-invariant subgroup of nilpotent group: Difference between revisions
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# <math>H</math> is a [[local powering-invariant subgroup]] of <math>G</math>. | # <math>H</math> is a [[local powering-invariant subgroup]] of <math>G</math>. | ||
===Equivalence of definitions== | ===Equivalence of definitions=== | ||
{{further|[[equivalence of definitions of powering-invariant subgroup of nilpotent group}} | {{further|[[equivalence of definitions of powering-invariant subgroup of nilpotent group]]}} | ||
Revision as of 06:57, 31 March 2013
This article describes a property that arises as the conjunction of a subgroup property: powering-invariant subgroup with a group property imposed on the ambient group: nilpotent group
View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup
Definition
A subgroup of a nilpotent group is termed a powering-invariant subgroup of nilpotent group if it satisfies the following equivalent conditions:
- is a powering-invariant subgroup of .
- is a local powering-invariant subgroup of .
Equivalence of definitions
Further information: equivalence of definitions of powering-invariant subgroup of nilpotent group