Category Archives: Veröffentlichungen

Veröffentlichung

Calculating the order of an invertible matrix

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Frank Celler and C. R. Leedham-Green
in L. Finkelstein and B. Kantor, editors, Groups and Computation II, volume 28 of Amer. Math. Soc DIMACS Series, 1997, pages 55-60

Abstract: In the first part of this note we present an algorithm for computing the order of an invertible matrix over a finite field and analyse its complexity. In the second part we compare this algorithm to the so-called spinning algorithm and give variations of the main algorithm to find the projective order and the p’-part, and to decide whether a given prime occurs in the order.

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A non-constructive recognition algorithm for the special linear and other classical groups

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Frank Celler and C. R. Leedham-Green,
in L. Finkelstein and B. Kantor, editors, Groups and Computation II, volume 28 of Amer. Math. Soc DIMACS Series, 1997, pages 61-67

Abstract: In the first part of this note we present a Monte Carlo algorithm that decides if a given set of matrices generates a group containing the special linear group. In the second part we give timings and extend the algorithm to the other classical groups.

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Generating Random Elements of a Finite Group

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Frank Celler, Charles R. Leedham-Green, Scott H. Murray, Alice C. Niemeyer, and E. A. O’Brien
Comm. Algebra, 23:4931-4948, 1995

Abstract: We present a practical algorithm to construct random elements of a matrix group. We analyse its theoretical behaviour and prove that asymptotically it produces uniformly distributed sequences of elements. We discuss tests to assess its effectiveness and use these to decide when its results are acceptable.

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A constructive recognition algorithm for the special linear group

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Frank Celler and C. R. Leedham-Green
Proceedings of the ATLAS Conference 1995

Abstract: In the first part of this note we present an algorithm to recognise constructively the special linear group. In the second part we give timings and examples.

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An algorithm for computing quotients of prime-power order for finitely presented groups and its implementation in GAP

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Frank Celler, M. F. Newman, Werner Nickel, and Alice C. Niemeyer
Technical Report 1993, School of Mathematical Sciences, Australian National University

Abstract: We describe an algorithm for computing quotients of prime-power order for finitely preseneted groups and its implementation in GAP. We use the opportunity (given by the design of the GAP language) to give rather more detail about such implementations than is available outside programs. We also describe some of the impact of this implementation process on the design of the GAP kernel.

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Kohomologie und Normalisatoren in GAP

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Frank Celler
diploma thesis 1992, RWTH Aachen

Abstract: I describe an algorithm for computing the first cohomology group of finite soluble groups, and give applications to the computation of normalizers and complements. The described algorithm are implemented in GAP.

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Some remarks on the computation of complements and normalizers in soluble groups

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F. Celler, J. Neubüser, and C. R. B. Wright
Topics in Computational Algebra 1990, Kluwer Academic Publishers, Dordrecht, 57-76

Abstract: We describe an algorithm for computing the first cohomology group of finite soluble groups, and give applications to the computation of normalizers and complements.

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