Perfect characteristic subgroup: Difference between revisions
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===Weaker properties=== | ===Weaker properties=== | ||
* [[Stronger than::Perfect IA-automorphism-invariant subgroup]] | |||
* [[Stronger than::IA-balanced subgroup]] | |||
* [[Stronger than::Perfect normal subgroup]] | * [[Stronger than::Perfect normal subgroup]] | ||
* [[Stronger than::Perfect subnormal subgroup]] | * [[Stronger than::Perfect subnormal subgroup]] | ||
Latest revision as of 13:32, 30 June 2009
This article describes a property that arises as the conjunction of a subgroup property: characteristic subgroup with a group property (itself viewed as a subgroup property): perfect group
View a complete list of such conjunctions
Definition
A subgroup of a group is termed a perfect characteristic subgroup if it satisfies the following equivalent conditions:
- It is perfect as a group and is a characteristic subgroup of the whole group.
- It is a characteristic subgroup of the whole group contained in the perfect core of the whole group.