Quasiprimitive 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 is a variation of primitivity|Find other variations of primitivity |
Definition
Symbol-free definition
A group is said to be quasiprimitive if it satisfies the following equivalent conditions:
- It possesses a faithful group action such that the restriction to every nontrivial normal subgroup is transitive
- It possesses a strongly contranormal subgroup, viz a subgroup whose product with every nontrivial normal subgroup is the whole group