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Some remarks on the computation of conjugacy classes of soluble groups

Published online by Cambridge University Press:  17 April 2009

M. Mecky  and
J. Neubüser
M. Mecky
Affiliation:
Lehrstuhl D für Mathematik, RWTH Aachen, D-5100 Aachen, Federal Republic of Germany
J. Neubüser
Affiliation:
Lehrstuhl D für Mathematik, RWTH Aachen, D-5100 Aachen, Federal Republic of Germany
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Abstract

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Laue et al have described basic algorithms for computing in a finite soluble group G given by an AG-presentation, among them a general algorithm for the computation of the orbits of such a group acting on some set Ω. Among other applications, this algorithm yields straightforwardly a method for the computation of the conjugacy classes of elements in such a group, which has been implemented in 1986 in FORTRAN within SOGOS by the first author and in 1987 in C within CAYLEY. However, for this particular problem one can do better, as discussed in this note.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 40 , Issue 2 , October 1989 , pp. 281 - 292
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Burnside, W., Theory of groups of finite order, 2nd ed (CUP, Cambridge, 1911).Google Scholar
[2]Cannon, J., ‘An introduction to the group theory language, Cayley’, in Computational Group Theory: Proc. LMS Symposium, Durham 1982, Editor Atkinson, M. (Academic Press, Florida, 1984). 146–183.Google Scholar
[3]Cannon, J., (private communication, 1987).Google Scholar
[4]Conlon, S. B., ‘Calculating characters of p-groups’, J. Sci Comput., (to appear). (University of Sydney 1987, Preprint).Google Scholar
[5]Felsch, V., ‘A machine independent implementation of a collection algorithm for the multiplication of group elements’, SYMSAC, 1976 (ACM 1976). Editor Jenks, R.D.159–166.Google Scholar
[6]Sandlöbes, C., ‘An interactive program for computing subgroups’, in Computational Group Theory: Proc. LMS Symposium, Durham 1982, Editor Atkinson, M. (Academic Press, Florida, 1984). 137–143.Google Scholar
[7]Felsch, V., ‘Comparing different collectors in SOGOS’, (Preliminary report, Lehrstuhl D für Mathematik, RWTH Aachen, 1988).Google Scholar
[8]Felsch, V. and Neubüser, J., ‘An algorithm for the computation of conjugacy classes and centralizers in p-groups’ 72: Lecture Note, in Comput. Sci. (Springer-Verlag, Berlin, Heidelberg, New York, 1979). 452–465.Google Scholar
[9]Glasby, S. P. and Slattery, M. C., ‘Computing intersections and normalizers in soluble groups’. (preprint).Google Scholar
[10]Havas, G. and Nicholson, T., ‘Collection’, in SYMSAC, 1976 (ACM, 1976), Editor Jenks, R.D.. 9–14.CrossRefGoogle Scholar
[11]Klass, M. J., ‘A generalization of Burnside's combinatorial lemma’, J. Combin. Theory Ser. A 20 (1976), 273–278.CrossRefGoogle Scholar
[12]Laue, R., Neubüser, J. and Schoenwaelder, U., ‘Algorithms for finite soluble groups and the SOGOS system’, in Computational Group Theory: Proc. LMS Symposium, Durham 1982, Editor Atkinson, M. (Academic Press, Florida, 1984). 105–135.Google Scholar
[13]Mecky, M., ‘SOGOS IV, Konjugiertenklassen’: Diplomarbeit (Lehrstuhl D für Mathematik, RWTH Aachen, 1989).Google Scholar
[14]Neubüser, J., Pahlings, H. and Plesken, W., ‘CAS; design and use of a system for the handling of characters of finite groups’, in Computational Group Theory: Proc. London Math. Soc. Symposium, Durham 1982, Editor Atkinson, M. (Academic Press, Florida, 1984). 195–247.Google Scholar
[15]Pahlings, H. and Plesken, W., ‘Group actions on Cartesian powers with application to representation theory’, J. Reine Angew. Math. 380 (1987), 178–195.Google Scholar
[16]Schneider, C., ‘Dixon's character table algorithm revisited’, (Universität Essen and University of Sydney. preprint).Google Scholar
[17]SOGOS Manual (Lehrstuhl D für Mathematik, RWTH Aachen, 1982); revised version 1988.Google Scholar
[18]Thiemann, P., ‘SOGOS III, Charaktere’: Diplomarbeit (Lehrstuhl D für Mathematik, RWTH Aachen, 1987).Google Scholar