论文信息 - Free Quotients of Finitely Presented Groups

Free Quotients of Finitely Presented Groups

We describe a computational, heuristic approach to the problem of deciding whether or not a given finitely presented group has a free quotient of rank two or more. Our strategy is to construct a finite nilpotent quotient of the given group, to search for quotients that are free within a variety containing that quotient, and then lift to the original group. We give theoretical justification to our strategy, and describe successful computations with sections of the Picard group SL2(Z[i]).

Derek F. Holt | Sarah Rees

[1] Warren Dicks,et al. Groups Acting on Graphs , 1989 .

[2] Hyman Bass,et al. Solution of the congruence subgroup problem for SLn (n ≥ 3) and Sp2n (n ≥ 2) , 1967 .

[3] Friedhelm Waldhausen,et al. Some problems on 3-manifolds , 1976 .

[4] Derek F. Holt,et al. A Graphics System for Displaying Finite Quotients of Finitely Presented Groups 113 , 1991, Groups And Computation.

[5] Richard G. Swan,et al. Generators and relations for certain special linear groups , 1968 .

[6] George Havas,et al. Application of computers to questions like those of Burnside , 1996 .

[7] R. Odoni,et al. Non-normal, standard subgroups of the Bianchi groups , 1996 .

[8] M. Hall. The Theory Of Groups , 1959 .