Just infinite group

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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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.
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View a list of other standard non-basic definitions

Definition

Symbol-free definition

A group is said to be just infinite if it satisfies the following equivalent conditions:

• It is infinite and every normal subgroup is of finite index
• It is infinite and every proper quotient is finite