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A primitive group with two regular minimal normal subgroups
Example
Primitive groups with two regular minimal normal subgroups do exist; the standard diagonal-type examples provide them.
Facts & Assumptions
Given: A standard faithful diagonal-type primitive action with socle for a nonabelian finite simple group .
In this action the left and right regular copies of are distinct minimal normal subgroups.
Distinct minimal normal subgroups of a finite faithful primitive group are regular (Two distinct minimal normal subgroups of a primitive group are regular).
Verification
The diagonal-type witness has two distinct minimal normal subgroups by [A1].
Applying [L1] to those two subgroups shows that both are regular. This is exactly the exceptional case allowed by the socle analysis.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
5 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Leonard H. Soicher, Primitive permutation groups (standard reference, not scraped)