---
title: "Bibliography"
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source: "https://docs.magma-maths.org/FiniteGroups/PermutationGroups/bibliography.md"
part: "Finite Groups"
chapter: "Permutation Groups"
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---

# Bibliography

<a id="cite-blocks-atkinson"></a>
- **[Atk75]** M.D. Atkinson. An algorithm for finding the blocks of a permutation group. *Math. Comp.*, 29:911–913, 1975.
<a id="cite-beals-phd"></a>
- **[Bea93]** G. Beals. *Algorithms for finite groups*. PhD thesis, University of Chicago, 1993.
<a id="cite-altsymrecog1"></a>
- **[BLGN+03b]** R. Beals, C. R. Leedham-Green, A. C. Niemeyer, C. E. Praeger, and A. Seress. A black-box algorithm for recognising finite symmetric and alternating groups, I. *Trans. Amer. Math. Soc.*, pages 2097–2113, 2003.
<a id="cite-bratus-pak"></a>
- **[BP00]** Sergey Bratus and Igor Pak. Fast constructive recognition of a black box group isomorphic to $S_n$ or $A_n$ using Goldbach's conjecture. *J. Symbolic Comp.*, 29:33–57, 2000.
<a id="cite-perm-matrix-i"></a>
- **[BC82]** G. Butler and J.J. Cannon. Computing with permutation and matrix groups I: Normal closure, commutator subgroups, series. *Math. Comp.*, 39:671–680, 1982.
<a id="cite-inductive-classes"></a>
- **[But94]** Greg Butler. An inductive schema for computing conjugacy classes in permutation groups. *Mathematics of Computation*, 62(205):363–383, 1994.
<a id="cite-butler-homs"></a>
- **[But85]** Gregory Butler. Effective computation with group homomorphisms. *J. Symbolic Comp.*, 1:143–157, 1985.
<a id="cite-two-trans"></a>
- **[CC91]** P.J. Cameron and J.J. Cannon. Recognizing doubly transitive groups. *J. Symb. Comp.*, 12(4/5):459–474, 1991.
<a id="cite-struct-gps"></a>
- **[CB92]** J.J. Cannon and W. Bosma. Structural computation in finite permutation groups. *CWI Quarterly*, 5(2):127–160, 1992.
<a id="cite-sylow-permg"></a>
- **[CCH97]** J.J. Cannon, B. Cox, and D.F. Holt. Computing Sylow subgroups in permutation groups. *J. Symb. Comp.*, 24(3/4):303–316, 1997.
<a id="cite-subgroups-permg"></a>
- **[CCH01b]** J.J. Cannon, B. Cox, and D.F. Holt. Computing the subgroups of a permutation group. *J. Symb. Comp.*, 31:149–161, 2001.
<a id="cite-chief-series-permg"></a>
- **[CH97]** J.J. Cannon and D.F. Holt. Computing chief series, composition series and socles in large permutation groups. *J. Symb. Comp.*, 24(3/4):285–301, 1997.
<a id="cite-autos-permg"></a>
- **[CH03]** J.J. Cannon and D.F. Holt. Automorphism group computation and isomorphism testing in finite groups. *J. Symbolic Comp.*, 35(3):241–267, 2003.
<a id="cite-maxsubgrp-permg"></a>
- **[CH04]** J.J. Cannon and D.F. Holt. Computing maximal subgroups of finite groups. *J. Symbolic Comp.*, 37(5):589–609, 2004.
<a id="cite-chss-lix"></a>
- **[CHSS03]** J. Cannon, D. Holt, M. Slattery, A. Steel. “Computing subgroups of low index in a finite group.” 2003.
<a id="cite-normal-subgps-permg"></a>
- **[CS]** J.J. Cannon and B. Souvignier. On the computation of normal subgroups in permutation groups. to appear, International Journal of Algebra and Computation.
<a id="cite-conj-classes-permg"></a>
- **[CS97]** J.J. Cannon and B. Souvignier. On the computation of conjugacy classes in permutation groups. In *Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation*, 392–399. Association for Computing Machinery, 1997. Maui, July 21–23, 1997.
<a id="cite-randomelements"></a>
- **[CLGM+95]** Frank Celler, Charles R. Leedham-Green, Scott H. Murray, Alice C. Niemeyer, and E. A. O'Brien. Generating random elements of a finite group. *Comm. Algebra*, 23(13):4931–4948, 1995.
<a id="cite-cfl-pointstabs"></a>
- **[CFL89]** G. Cooperman, L. Finkelstein, and E.M. Luks. Reduction of group constructions to point stabilizers. In *Proc. of International Symposium on Symbolic and Algebraic Computation ISSAC '89*, 351–356. ACM, 1989.
<a id="cite-gebhardt-presentations"></a>
- **[Geb00]** Volker Gebhardt. Constructing a short defining set of relations for a finite group. *J. Algebra*, 233:526–542, 2000.
<a id="cite-holt-multiplier"></a>
- **[Hol84]** D.F. Holt. The calculation of the Schur multiplier of a permutation group. In *Computational group theory (Durham, 1982)*, 307–319. Academic Press, London, 1984.
<a id="cite-holt-cover"></a>
- **[Hol85a]** D.F. Holt. A computer program for the calculation of a covering group of a finite group. *J. Pure Appl. Algebra*, 35(3):287–295, 1985.
<a id="cite-holt-cohom"></a>
- **[Hol85b]** D.F. Holt. The mechanical computation of first and second cohomology groups. *J. Symbolic Comp.*, 1(4):351–361, 1985.
<a id="cite-hulpkelinton"></a>
- **[HL03]** Alexander Hulpke and Steve Linton. Total ordering on subgroups and cosets. In *Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation*, 156–160. ACM, New York, 2003. URL: [https://doi.org/10.1145/860854.860892](https://doi.org/10.1145/860854.860892), [doi:10.1145/860854.860892](https://doi.org/10.1145/860854.860892).
<a id="cite-altsymrecogn"></a>
- **[JLNP13]** S Jambor, M Leuner, A. C. Niemeyer, and W Plesken. Fast recognition of alternating groups of unknown degree. *J. Algebra*, 392:315–335, 2013.
<a id="cite-kantor-comp-factors"></a>
- **[Kan91]** William M. Kantor. Finding composition factors of permutation groups of degree $n\leq 10\sp 6$. *J. Symbolic Comp.*, 12(4/5):517–526, 1991.
<a id="cite-lnps-jellyfish"></a>
- **[LNPS06]** M. Law, A.C. Niemeyer, C.E. Praeger, and A. Seress. A reduction algorithm for for large-base primitive permutation groups. *LMS J. Comput. Math.*, 9:159–173, 2006.
<a id="cite-grp-homs"></a>
- **[LGPS91]** C.R. Leedham-Green, C.E. Praeger, and L.H. Soicher. Computing with group homomorphisms. *J. Symbolic Comp.*, 12(4/5):527–532, 1991.
<a id="cite-leon3"></a>
- **[Leo80]** Jeffrey S. Leon. On an algorithm for finding a base and a strong generating set for a group given by generating permutations. *Math. Comp.*, 35(151):941–974, 1980.
<a id="cite-leon2"></a>
- **[Leo97]** Jeffrey S. Leon. Partitions, refinements, and permutation group computation. In Larry Finkelstein and William M. Kantor, editors, *Groups and Computation II*, volume 28 of Dimacs series in Discrete Mathematics and Computer Science, 123–158. Providence R.I., 1997. Amer. Math. Soc.
<a id="cite-luks-polynomial"></a>
- **[Luk93]** E.M. Luks. Permutation groups and polynomial-time computation. In *Groups and computation (New Brunswick, NJ, 1991)*, volume 11 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 139–175. Amer. Math. Soc., 1993.
<a id="cite-bdm-nauty-paper"></a>
- **[McK81]** B. D. McKay. Practical Graph Isomorphism. *Congressus Numerantium*, 30:45–87, 1981.
<a id="cite-mecky-neubuser"></a>
- **[MN89]** M. Mecky and J. Neubüser. Some remarks on the computation of conjugacy classes of soluble groups. *Bull. Austral, Math. Soc.*, 40(2):281–292, 1989.
<a id="cite-minkwitz"></a>
- **[Min98]** Torsten Minkwitz. An algorithm for solving the factorization problem in permutation groups. *J. Symbolic Comput.*, 26(1):89–95, 1998. URL: [https://doi.org/10.1006/jsco.1998.0202](https://doi.org/10.1006/jsco.1998.0202), [doi:10.1006/jsco.1998.0202](https://doi.org/10.1006/jsco.1998.0202).
<a id="cite-neumann-algs-permg"></a>
- **[Neu86]** P.M. Neumann. Some algorithms for computing with finite permutation groups. In C.M. Campbell E.F. Robertson, editor, *Groups - St. Andrews 1985*, number 121 in London Math. Soc. Lecture Notes Series. 1986.
<a id="cite-jimr-msc"></a>
- **[Ric73]** J.S. Richardson. Group: a computer system for group-theoretic calculations. Master's thesis, Department of Pure Mathematics, University of Sydney, September 1973.
<a id="cite-schmalz-ladder"></a>
- **[Sch90a]** Bernd Schmalz. Verwendung von Untergruppenleitern zur Bestimmung von Doppelnebenklassen. *Bayreuther Mathematische Schriften*, 31:109–143, 1990.
<a id="cite-blocks-schonert-seress"></a>
- **[SS94]** M. Schönert and A. Seress. Finding blocks of imprimitivity in small-base groups in nearly linear time. In *Proc. 1994 ACM-SIGSAM Inter. Symp. on Symbolic and Algebraic Comp.*, 154–157. 1994.
<a id="cite-seress2003"></a>
- **[Ser03]** Ákos Seress. *Permutation Group Algorithms*. Volume 152 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 2003. ISBN 0-521-66103-X. URL: [http://dx.doi.org/10.1017/CBO9780511546549](http://dx.doi.org/10.1017/CBO9780511546549), [doi:10.1017/CBO9780511546549](https://doi.org/10.1017/CBO9780511546549).
<a id="cite-sol-schreier"></a>
- **[Sim90]** Charles C. Sims. Computing the order of a solvable permutation group. *J. Symb. Comp.*, 9(5/6):699–705, 1990.
<a id="cite-chief-series-unger"></a>
- **[Ung]** W.R. Unger. Computing chief series of a large permutation group. In preparation.
<a id="cite-chtr-table-unger"></a>
- **[Ung06a]** W.R. Unger. Computing the character table of a finite group. *J. Symbolic Comp.*, 41(8):847–862, 2006.
<a id="cite-unger"></a>
- **[Ung06b]** W.R. Unger. Computing the solvable radical of a permutation group. *J. Algebra*, 300(1):305–315, 2006.