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The groups of order at most 2000
 Electronic Research Announcements of the American Mathematical Society
, 2001
"... (Communicated by Efim Zelmanov) Abstract. We announce the construction up to isomorphism of the 49 910 529 484 groups of order at most 2000. 1. ..."
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(Communicated by Efim Zelmanov) Abstract. We announce the construction up to isomorphism of the 49 910 529 484 groups of order at most 2000. 1.
Parallel Construction of Finite Solvable Groups
"... An algorithm for the construction of finite solvable groups of small order is given. A parallelized version under PVM is presented. ..."
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An algorithm for the construction of finite solvable groups of small order is given. A parallelized version under PVM is presented.
Construction of Combinatorial Objects
, 1995
"... Isomorphism problems often can be solved by determining orbits of a group acting on the set of all objects to be classified. The paper centers around algorithms for this topic and shows how to base them on the same idea, the homomorphism principle. Especially it is shown that forming Sims chains, u ..."
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Isomorphism problems often can be solved by determining orbits of a group acting on the set of all objects to be classified. The paper centers around algorithms for this topic and shows how to base them on the same idea, the homomorphism principle. Especially it is shown that forming Sims chains, using an algorithmic version of Burnside's table of marks, computing double coset representatives, and computing Sylow subgroups of automorphism groups can be explained in this way. The exposition is based on graph theoretic concepts to give an easy explanation of data structures for group actions.