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Mathematics of Computation

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A space efficient algorithm for group structure computation

Author: Edlyn Teske
Journal: Math. Comp. 67 (1998), 1637-1663
MSC (1991): Primary 11Y16
MathSciNet review: 1474658
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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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Additional Information

Edlyn Teske
Affiliation: Technische Universität Darmstadt, Institut für Theoretische Informatik, Alexanderstraße 10 64283 Darmstadt Germany
Address at time of publication: Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

Keywords: Generic algorithms; group structure computation; Pollard’s $\rho$-method; class groups
Received by editor(s): February 7, 1997
Received by editor(s) in revised form: April 23, 1997
Article copyright: © Copyright 1998 American Mathematical Society