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A Space Efficient Algorithm for Group Structure Computation

Edlyn Teske
Mathematics of Computation
Vol. 67, No. 224 (Oct., 1998), pp. 1637-1663
Stable URL: http://www.jstor.org/stable/2584867
Page Count: 27
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Space Efficient Algorithm for Group Structure Computation
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Abstract

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($\sqrt{n}$) (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.

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