Core-characteristic subgroup: Difference between revisions
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{{subgroup property}} | {{subgroup property}} | ||
==Definition== | |||
{{quick phrase|[[quick phrase::intersection of all conjugates is characteristic]], [[quick phrase::normal core is characteristic]]}} | |||
===Symbol-free definition=== | ===Symbol-free definition=== | ||
A [[subgroup]] of a [[group]] is termed '''core-characteristic''' if its [[normal core]] is a [[characteristic subgroup]] of the whole group. | A [[subgroup]] of a [[group]] is termed '''core-characteristic''' if its [[defining ingredient::normal core]] is a [[defining ingredient::characteristic subgroup]] of the whole group. | ||
===Definition with symbols=== | ===Definition with symbols=== | ||
Revision as of 23:36, 11 January 2010
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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
QUICK PHRASES: intersection of all conjugates is characteristic, normal core is characteristic
Symbol-free definition
A subgroup of a group is termed core-characteristic if its normal core is a characteristic subgroup of the whole group.
Definition with symbols
A subgroup of a group is termed core-characteristic if the normal core of in is a characteristic subgroup of .
Relation with other properties
Stronger properties
- Characteristic subgroup
- Automorph-conjugate subgroup
- Intersection of automorph-conjugate subgroups
- Core-free subgroup
Conjunction with other properties
Any normal subgroup that is also core-characteristic, is characteristic.