Summary
We show that the problem of computing a basis for an abelian transitive permutation group is in N C k and also we show that the problem of computing a basis for an abelian permutation group and the problem of computing the intersection of two abelian groups acting on n points, can be solved in depth (log n)k on a Monte Carlo Boolean circuit of polynomial size. Moreover the latter two problems are shown to be in N C k in the restricted case of bounded number of generators.
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Iliopoulos, C.S. Monte Carlo circuits for the abelian permutation group intersection problem. Acta Informatica 23, 697–705 (1986). https://doi.org/10.1007/BF00264315
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DOI: https://doi.org/10.1007/BF00264315