Extension-closed group property

From Groupprops
Jump to: navigation, search
This article defines a group metaproperty: a property that can be evaluated to true/false for any group property
View a complete list of group metaproperties


Suppose \alpha is a group property. We say that \alpha is extension-closed if the following holds:

For any group G and normal subgroup H of G such that both H and the quotient group G/H satisfy the property \alpha, G also satisfies the property \alpha.


Locally finite group, Noetherian group, Periodic group, Solvable group