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Intermediately fully invariant subgroup

65 bytes added, 02:53, 22 May 2009
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===Symbol-free definition===
A [[subgroup]] of a [[group]] is termed '''intermediately fully invariant''' or '''intermediately fully characteristic''' if it is [[defining ingredient::fully characteristic invariant subgroup|fully characteristicinvariant]] in every intermediate subgroup of the group containing it.
===Definition with symbols===
A subgroup <math>H</math> of a group <math>G</math> is termed '''intermediately fully invariant''' or '''intermediately fully characteristic''' in <math>G</math> if, for any intermediate subgroup <math>K</math> of <math>G</math>, <math>H</math> is fully characteristic in <math>K</math>: for any [[endomorphism]] <math>\varphi</math> of <math>K</math>, <math>\varphi(H) \le H</math>.
==Relation with other properties==
===Weaker properties===
* [[Stronger than::Fully characteristic invariant subgroup]]
* [[Stronger than::Intermediately characteristic subgroup]]
* [[Stronger than::Characteristic subgroup]]
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