Pin showed that every p-state automaton (p a prime) containing a cyclic permutation and a non-permutation has a synchronizing word of length at most (p - 1){sup}2. In this paper, we consider permutation automata with the property that adding any non-permutation will lead to a synchronizing word and establish bounds on the lengths of such synchronizing words. In particular, we show that permutation groups whose permutation character over the rationals splits into a sum of only two irreducible characters have the desired property.
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