67.53 References

[1] 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, 4931--4948, 1995.

[2] Frank Celler and C.R. Leedham-Green, ``Calculating the Order of an Invertible Matrix'', ``Groups and Computation II'', Amer. Math. Soc. DIMACS Series 28, 1997.

[3] Frank Celler and C.R. Leedham-Green, ``A Non-Constructive Recognition Algorithm for the Special Linear and Other Classical Groups'', ``Groups and Computation II'', Amer. Math. Soc. DIMACS Series 28, 1997.

[4] Frank Celler and C.R. Leedham-Green, ``A constructive recognition algorithm for the special linear group'', preprint.

[5] Derek F. Holt and Sarah Rees, ``Testing modules for irreducibility'', J. Austral. Math. Soc. Ser. A, 57, 1--16, 1994.

[6] Derek F. Holt, C.R. Leedham-Green, E.A. O'Brien, and Sarah Rees, ``Computing Matrix Group Decompositions with Respect to a Normal Subgroup'', J. Algebra 184, 818--838, 1996.

[7] Derek F. Holt, C.R. Leedham-Green, E.A. O'Brien, and Sarah Rees, ``Testing Matrix Groups for Imprimitivity'', J. Algebra 184, 795--817, 1996.

[8] C.R. Leedham-Green and E.A. O'Brien, ``Tensor Products are Projective Geometries'', to appear J. Algebra.

[9] C.R. Leedham-Green and E.A. O'Brien, ``Recognising tensor products of matrix groups'', to appear Internat. J. Algebra Comput.

[10] Scott H. Murray and E.A. O'Brien, ``Selecting Base Points for the Schreier-Sims Algorithm for Matrix Groups'', J. Symbolic Comput. 19, 577--584, 1995.

[11] Alice C. Niemeyer and Cheryl E. Praeger ``A Recognition Algorithm for Classical Groups over Finite Fields'', submitted to Proceedings of the London Mathematical Society.

[12] Alice C. Niemeyer and Cheryl E. Praeger ``Implementing a Recognition Algorithm for Classical Groups'', ``Groups and Computation II'', Amer. Math. Soc. DIMACS Series 28, 1997.

[13] Anthony Pye, ``Recognising reducible matrix groups'', in preparation.

The following sources provide additional theoretical background to the algorithms.

[14] M. Aschbacher (1984), ``On the maximal subgroups of the finite classical groups'', Invent. Math. 76, 469--514, 1984.

[15] Peter Kleidman and Martin Liebeck, ``The Subgroup Structure of the Finite Classical Groups'', Cambridge University Press, London Math. Soc. Lecture Note Series 129, 1990.

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GAP 3.4.4
April 1997