2-groups with an odd-order automorphism that is the identity by Mazurov V.D.

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By Mazurov V.D.

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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 S such that a = cr _1 . An involution over V* which is a morphism is called a Watson-Crick morphism over the alphabet V, and is denoted by £. If £(a) = b, then we say that a and b are complementary to each other. Remember that the DNA alphabet consists of four letters, VDNA = {A,C, G,T}, which are abbreviations for the four nucleotides: adenine, cytosine, guanine, thymine, and £,(A) = T, £(C) = G. In what follows, all the alphabets we use will be of an even cardinality (they are formed by pairs of complementary letters) bigger than or equal to 4.

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