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For groups represented as permutations. Group transitivity, rank 3 groups, orbits and suborbits, stablizers, permutation characters, primitivity are all on-topic.
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Effect on finite transformation semigroup under a particular modification of the generators
The following question arises in connection with problems in automata theory related to the road problem. Let $f_1, f_2: [N] \to [N]$ be maps such that the transformation semigroup $S = \langle f_1, f …