Innately transitive 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
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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
This is a variation of primitivity|Find other variations of primitivity |

Definition

Symbol-free definition

A group is said to be innately transitive if the following equivalent conditions hold:

The plinth theorem states that there are at most two minimal normal subgroups acting transitively, and that they must be isomorphic; in fact, they must be conjugate by a permutation on the set on which the group is acting.

Definition with symbols

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Relation with other properties

Stronger properties