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A Space Efficient Algorithm For Group Structure Computation

By Edlyn Teske


. We present a new algorithm for computing the structure of a finite abelian group, which has to store only a fixed, small number of group elements, independent of the group order. We estimate the computational complexity by counting the group operations such as multiplications and equality checks. Under some plausible assumptions, we prove that the expected run time is O( p n) (with n denoting the group order), and we explicitly determine the O- constants. We implemented our algorithm for ideal class groups of imaginary quadratic orders and present experimental results. 1. Introduction Let G be a finite abelian group, written multiplicatively, for which we assume the following: ffl For a; b 2 G we can compute c = a b and we can test whether a = b. ffl We know the neutral element 1 2 G. ffl There is a computable function f : G ! f1; : : : ; 20g such that 20 X i=1 fi fi fi fi #fa 2 G : f(a) = ig \Gamma jGj 20 fi fi fi fi = O( p jGj); where jGj denotes group order. Thr..

Year: 1998
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