Efficient multiplication algorithms for finite polycyclic groups
نویسنده
چکیده
Let G be a finite soluble group given by a reduced confluent polycyclic presentation. Represent group elements by reduced words. Then there exists an algorithm for multiplying two group elements which has subexponential running time and requires polynomial space. Moreover, given the prime factorisation of the group order, the problem of multiplying two group elements is probabilistically polynomial time equivalent to the same problem for p-groups, where p divides the order of G. Classification (AMS 2000): 20-04, 20D10, 68W40
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