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Representing subgroups of finitely presented groups by quotient subgroups. (English) Zbl 1062.20037
Summary: This article proposes to represent subgroups of finitely presented groups by their image in a quotient. It gives algorithms for basic operations in this representation and investigates how iteration of this approach can be used to extend known quotient groups with a solvable normal subgroup.

MSC:
20F05 Generators, relations, and presentations of groups
20-04 Software, source code, etc. for problems pertaining to group theory
20E07 Subgroup theorems; subgroup growth
68W30 Symbolic computation and algebraic computation
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References:
[1] Baumeister B., Math. Proc. Cambridge Philos. Soc. 128 (1) pp 21– (2000) · Zbl 0954.51005
[2] Baumslag G., J. Algebra 142 (1) pp 118– (1991) · Zbl 0774.20019
[3] Breuer, T. and Linton, S. ”The GAP 4 type system: Organising algebraic algorithms”. Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation (ISSAC 1998). 1998, Rostock, Germany. Edited by: gloo, O. pp.38–45. New York: ACM Press. [Breuer and Linton 1998] · Zbl 0918.68050
[4] Brückner H., Dissertation, in: Algorithmen für endliche auflösbare Gruppen und Anwendungen (1998)
[5] Celler F., ”XGAP: GAP4 share package” (1999)
[6] GAP: Groups, algorithms, and programming, Version 4.2 (2000)
[7] Havas G., A Reidemeister–Schreier program (Canberra, 1973) (1974)
[8] Havas G., Groups and computation (New Brunswick, NJ, 1991) pp 29– (1993)
[9] Holt D. F., Computational group theory (Durham, 1982) pp 307– (1984)
[10] Holt D. F., J. Pure Appl. Algebra 35 (3) pp 287– (1985) · Zbl 0552.20006
[11] Holt D. F., Groups, combinatorics and geometry pp 459– (1992)
[12] Holt D. F., Groups and computation (New Brunswick, NJ, 1991) pp 113– (1993) · Zbl 0808.20008
[13] Holt D. F., ”Smash: matrix groups and G-modules” (1995)
[14] Hulpke A., Ph.d. thesis, in: Konstruktion transitiver Permutations gruppen (1996) · Zbl 0955.20002
[15] Huppert B., Endliche Gruppen (1967) · Zbl 0217.07201
[16] Jansen C., An atlas of Brauer characters (1995) · Zbl 0831.20001
[17] Krasner M., Acta. Sci. Math. (Szeged) 14 pp 39– (1951)
[18] Leedham-Green C. R., J. Symbolic Comput. 12 pp 527– (1991) · Zbl 0789.20001
[19] Lo E. H., J. Symbolic Comput. 25 (1) pp 61– (1998) · Zbl 0930.20037
[20] Macdonald I. D., J. Austral. Math. Soc. Ser. A 17 pp 102– (1974) · Zbl 0277.20024
[21] ”Magnus: A system for exploring infinite groups” (1997)
[22] Magnus W., Combinatorial group theory: Presentations of groups in terms of generators and relations (1966) · Zbl 0138.25604
[23] Neubüser J., LMS Lecture Note Series 71, in: Groups – St. Andrews pp 1– (1981)
[24] Nickel W., Geometric and computational perspectives on infinite groups(Minneapolis and New Brunswick, 1994) pp 175– (1996)
[25] Niemeyer A. C., J. Symbolic Comput. 18 (6) pp 541– (1994) · Zbl 0844.20002
[26] Pasechnik D., ”Abelian factors of the kernel of a homomorphism” (1998)
[27] Plesken W., J. Symbolic Comput. 4 (1) pp 111– (1987) · Zbl 0635.20013
[28] Remak R., J. Reine Angew. Math. 163 pp 1– (1930)
[29] Robinson D. J. S., A course in the theory of groups,, 2. ed. (1996)
[30] Schur I., J. Reine Angew. Math. 132 pp 85– (1907)
[31] Sims C. C., Computation with finitely presented groups (1994) · Zbl 0828.20001
[32] Todd J. A., Proc. Edinburgh Math. Soc. 5 pp 26– (1936) · Zbl 0015.10103
[33] Wamsley, J. W. ”Computation in nilpotent groups (theory)”. Proceedings of the Second International Conference on the Theory of Groups. Canberra. Edited by: Newman, M. F. pp.691–700. Berlin: Springer. [Wamsley 1974], Lecture Notes in Math. 372 · Zbl 0288.20031
[34] Wilson R. A., ”Atlas of finite group representations” (1996)
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