By Mazurov V.D.

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**Additional resources for 2-groups with an odd-order automorphism that is the identity on involutions**

**Example text**

If all the intersections in line (4) are finite sets, then one can compute the values k(t, q, s,p) from line (8). Therefore, we have an algorithm. Let us say a few words about its correctness. If in line (4) the intersection L(t, q) n£(£(s,p)) is infinite for some t,q,s,p £ Q and (q, s) £ S, then there are arbitrarily many strings z = uvx£,(v)y £ L with v £ L(t,q) and £(v) £ L(s,p), which implies that L is not loop-free. Remember that the automaton is minimal so that there must exist a path, empty or not, from go to t as well as one from p to a state in F.

An involution over a set S is a bijective mapping

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