Let $Q= \{q_1,\ldots,q_n\}$ be a set of permutations of some finite set $X$. Let $Q' = \{q \in Q^* \mid q=1\in S_X\}$, where $S_X$ is the symmetric group on $X$. Is $Q'$ a regular language?
regular languages and permutations
2
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group-theory