An introduction to the Group Theory Language, Cayley. CAYLEY is a high level programming language which has been developed by the author to allow easy access to a collectionn of algorithms for doing calculations in groups and related structures. This paper gives a useful introduction to the language. There is a description of some of the features of the language and there are lists of some of the algorithms it incorporates. Four sample CAYLEY programs are given: a test for nonregularity of groups of prime-power order; a test for simplicity of finite groups; calculation of transfer; calculation of a presentation of a knot group. CAYLEY is easy and comfortable to use. As the sample programs show, novel approaches may be needed to use it efficiently.

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 109 articles , 2 standard articles )

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  1. Prins, A.L.; Fray, R.L.: The Fischer-Clifford matrices of an extension group of the form $2^7:(2^5:S_6)$. (2014)
  2. De Vos, Alexis: Reversible computing. Fundamentals, quantum computing, and applications. (2010)
  3. Kilford, L. J. P.: Modular forms. A classical and computational introduction (2008)
  4. Roney-Dougal, Colva M.: The primitive permutation groups of degree less than 2500. (2005)
  5. Everitt, Brent: 3-manifolds from Platonic solids. (2004)
  6. Cannon, John J.; Holt, Derek F.: Automorphism group computation and isomorphism testing in finite groups (2003)
  7. Gottschalk, Harald; Leemans, Dimitri: Geometries for the group PSL$(3,4)$ (2003)
  8. Özkan, Engin; Aydın, Hüseyin; Dikici, Ramazan: Applications of Fibonacci sequences in a finite nilpotent group. (2003)
  9. Roney-Dougal, Colva M.; Unger, William R.: The affine primitive permutation groups of degree less than 1000. (2003)
  10. Lomonaco jun., Samuel J.; Kauffman, Louis H.: Quantum hidden subgroup algorithms: a mathematical perspective (2002)
  11. Gollan, Holger W.: A new existence proof for $Ly$, the sporadic simple group of R. Lyons (2001)
  12. Otto, Friedrich: A survey on the computational power of some classes of finite monoid presentations (2000)
  13. An, Jianbei: The Alperin and Dade conjectures for the simple Conway’s third group (1999)
  14. Beals, Robert: Algorithms for matrix groups and the Tits alternative (1999)
  15. Coleman, Donald B.; Sandling, Robert: Mod $2$ group algebras with metabelian unit groups (1998)
  16. Starostin, A.I.: Finite $p$-groups (1998)
  17. An, Jianbei: The Alperin and Dade conjectures for the simple Held group (1997)
  18. Boyvalenkov, Peter; Nikova, Svetla: On lower bounds on the size of designs in compact symmetric spaces of rank 1 (1997)
  19. Burns, J.; Ellis, G.; MacHale, D.; Ó Murchú, P.; Sheehy, R.; Wiegold, J.: Lower central series of groups with small upper central factors (1997)
  20. Edjvet, Martin; Thomas, Richard M.: The groups $(l,m\mid n,k)$ (1997)

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