×
Hulpke, Alexander

Representing subgroups of finitely presented groups by quotient subgroups. (English) Zbl 1062.20037

Exp. Math. 10, No. 3, 369-381 (2001).
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.

Cited in 3 Documents

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

Keywords:

subgroups of finitely presented groups; images in quotient groups; algorithms; solvable normal subgroups

Software:

GAP; ATLAS Group Representations; QUOTPIC
Cite Review PDF
Full Text: DOI Euclid EuDML

References:

[1] Baumeister B., Math. Proc. Cambridge Philos. Soc. 128 (1) pp 21– (2000) · Zbl 0954.51005 · doi:10.1017/S0305004199004028
[2] Baumslag G., J. Algebra 142 (1) pp 118– (1991) · Zbl 0774.20019 · doi:10.1016/0021-8693(91)90221-S
[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 · doi:10.1016/0022-4049(85)90046-5
[11] Holt D. F., Groups, combinatorics and geometry pp 459– (1992) · doi:10.1017/CBO9780511629259.040
[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 · doi:10.1007/978-3-642-64981-3
[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 · doi:10.1016/S0747-7171(08)80102-2
[19] Lo E. H., J. Symbolic Comput. 25 (1) pp 61– (1998) · Zbl 0930.20037 · doi:10.1006/jsco.1997.0167
[20] Macdonald I. D., J. Austral. Math. Soc. Ser. A 17 pp 102– (1974) · Zbl 0277.20024 · doi:10.1017/S1446788700015962
[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 · doi:10.1006/jsco.1994.1064
[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 · doi:10.1016/S0747-7171(87)80060-3
[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) · doi:10.1007/978-1-4419-8594-1
[30] Schur I., J. Reine Angew. Math. 132 pp 85– (1907)
[31] Sims C. C., Computation with finitely presented groups (1994) · Zbl 0828.20001 · doi:10.1017/CBO9780511574702
[32] Todd J. A., Proc. Edinburgh Math. Soc. 5 pp 26– (1936) · Zbl 0015.10103 · doi:10.1017/S0013091500008221
[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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.