A primitive group action is transitive and it has no nontrivial group blocks. A transitive group action that is not primitive is called imprimitive. A group that has a faithful primitive group action is called a primitive group.
Primitive Group Action
See also
Group, Group Block, Primitive Group, Socle, Transitive Group, Transitive Group ActionThis entry contributed by Todd Rowland
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Rowland, Todd. "Primitive Group Action." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/PrimitiveGroupAction.html