Kohomologie und Normalisator

• F. Celler, J. Neubüser, and C. R. B. Wright,
  Some remarks on the computation of complements and normalizers in soluble groups,
  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.

  Preprint: DVI file (33KByte), PostScript file (93KByte) or PDF (234 KByte).

• Frank Celler,
  Kohomologie und Normalisatoren in GAP,
  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.

  In German: DVI file (110KByte), PostScript file (236KByte) or PDF (948 KByte).

• Frank Celler, M. F. Newman, Werner Nickel, and Alice C. Niemeyer,
  An algorithm for computing quotients of prime-power order for finitely presented groups and its implementation in GAP,
  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.

  Preprint: DVI file (61KByte), PostScript file (151KByte) or PDF (454 KByte).

Matrixgruppen

• 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

  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.

  Preprint: DVI file (24KByte), PostScript file (76KByte) or PDF (205 KByte).

• Frank Celler and C. R. Leedham-Green,
  A constructive recognition algorithm for the special linear group,
  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.

  Preprint: DVI file (24KByte), PostScript file (61KByte) or PDF (229 KByte).

• Frank Celler,
  Konstruktive Erkennungsalgorithmen klassischer Gruppen in GAP,
  Phd. Thesis, RWTH Aachen

  In German: DVI file (123KByte), PostScript file (227KByte) or PDF (1 MByte).

• Frank Celler and C. R. Leedham-Green,
  Calculating the order of an invertible matrix,
  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.

  Preprint: DVI file (13KByte), PostScript file (36KByte) or PDF (189 KByte).

• Frank Celler and C. R. Leedham-Green,
  A non-constructive recognition algorithm for the special linear and other classical groups,
  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.

  Preprint: DVI file (13KByte), PostScript file (36KByte) or PDF ( 184KByte).