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A polycyclic quotient algorithm. (English) Zbl 0930.20037
An algorithm to compute polycyclic quotients of a group given by a finite presentation is discussed. The algorithm is based on a generalization of the Gröbner basis method to the integral group ring of a polycyclic group. Most of this material can be found in the author’s thesis (Rutgers Univ., 1996). A simplified version of this paper is also available [in DIMACS, Ser. Discrete Math. Theor. Comput. Sci. 28, 159-167 (1997; Zbl 0874.20020)].

20F14 Derived series, central series, and generalizations for groups
20-04 Software, source code, etc. for problems pertaining to group theory
20F05 Generators, relations, and presentations of groups
20C07 Group rings of infinite groups and their modules (group-theoretic aspects)
68W30 Symbolic computation and algebraic computation
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