Lower central series condition: Difference between revisions
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{{subgroup | {{subgroup metaproperty}} | ||
==Definition== | ==Definition== | ||
A [[subgroup property]] <math>p</math> is said to satisfy the '''lower central series''' condition if, whenever <math>H \le G</math> is a [[subgroup]] satisfying property <math>p</math>, we have that <math>\gamma_k(H)</math> satisfies property <math>p</math> in <math>\gamma_k(G)</math> for all positive integers <math>k</math>. | A [[subgroup property]] <math>p</math> is said to satisfy the '''lower central series''' condition if, whenever <math>H \le G</math> is a [[subgroup]] satisfying property <math>p</math>, we have that <math>\gamma_k(H)</math> satisfies property <math>p</math> in <math>\gamma_k(G)</math> for all positive integers <math>k</math>. | ||
Revision as of 15:12, 3 July 2013
This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property
View a complete list of subgroup metaproperties
View subgroup properties satisfying this metaproperty| View subgroup properties dissatisfying this metaproperty
VIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions
Definition
A subgroup property is said to satisfy the lower central series condition if, whenever is a subgroup satisfying property , we have that satisfies property in for all positive integers .
