Just infinite group

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

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
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