View source for Sub-central factor of normalizer

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{{subgroup property}}

==Definition==

===Definition with symbols===

A [[subgroup]] <math>H</math> of a [[group]] <math>G</math> is termed a '''sub-central factor of normalizer''' if there exists an ascending chain:

<math>H = H_0 \le H_1 \le \ldots \le H_n = G</math>

such that each <math>H_i</math> is a [[central factor of normalizer]] of <math>H_{i+1}</math>.

==Formalisms==

{{obtainedbyapplyingthe|subordination operator|central factor of normalizer}}

==Relation with other properties==

===Stronger properties===

* [[Weaker than::Central factor of normalizer]]
** [[Weaker than::Central factor]]
** [[Weaker than::Self-normalizing subgroup]]
==Metaproperties==

{{transitive}}