The Group Properties Wiki (pre-alpha)
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Quotient-closed group property
From Groupprops
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
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This article is about a definition in group theory that is standard among the group theory community (or sub-community that dabbles in such things) but is not very basic or common for people outside
VIEW: Definitions built on this | Facts about this | Survey articles about this
View a list of other standard non-basic definitions
Definition
Symbol-free definition
A group property is said to be quotient-closed or Q-closed if any quotient of a group satisfying the property must also satisfy the property.
Definition with symbols
A group property p is said to be quotient-closed or Q-closed if whenever G satisfies property p, and N is a normal subgroup of G, the quotient group G / N must also satisfy property p.
Relation with other metaproperties
Stronger metaproperties
