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On Deciding Finiteness for Matrix Groups over Fields of Positive Characteristic

Published online by Cambridge University Press:  01 February 2010

A. Detinko
A. Detinko
Affiliation:
Department of Applied Mathematics, Polotsk State University, Novopolotsk, Belarus, 211440, [email protected]

Abstract

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The author considers the development of algorithms for deciding whether a finitely generated matrix group over a field of positive characteristic is finite. A deterministic algorithm for deciding the finiteness is presented for the case of a field of transcendence degree one over a finite field.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 4 , 2001 , pp. 64 - 72
Copyright
Copyright © London Mathematical Society 2001

References

1.Babai, L., Beals, R. and Rockmore, D., ‘Deciding finiteness of matrix groups in deterministic polynomial time’, Proc. ISSAC '93 (ACM Press, 1993) 117–126.CrossRefGoogle Scholar
2.Beals, R., ‘Algorithms for matrix groups and the Tits alternative’, Proc. 36th IEEE FOCS (IEEE, 1995) 593–602.Google Scholar
3.Ivanyos, G., ‘Algorithms for algebras over global fields’, Ph.D. Thesis, Hungarian Academy of Science, 1996.Google Scholar
4.Jakobson, M., Structure of rings (Amer. Math. Soc, Providence, RI, 1956).Google Scholar
5.Lidl, R. and Niederreiter, H., Finite fields (Addison-Wesley, Reading, MA, 1983).Google Scholar
6.Schönert, M. et al. , GAP—Groups, algorithms and programming, 5th edn (Rheinisch-Westfällische Technische Hochschule, Aachen, Germany, 1995).Google Scholar
7.Rockmore, D., TAN, K.-S. and Beals, R., ‘Deciding finiteness for matrix groups over function fields’, Israeli. Math. 109 (1999) 93–116.Google Scholar
8.Seress, A., ‘An introduction to computational group theory’, Notices Amer. Math. Soc. 44 (1997) 671–679.Google Scholar
9.Suprunenko, D., Matrix groups, Trans. Math. Monographs 45 (Amer. Math. Soc, Providence, RI, 1976).Google Scholar
10.Zalesskii, A. E., ‘Maximal periodic subgroups of the general linear group over a field of positive characteristic’, Vestsi Akad. Navuk BSSR Sen Fiz.-Mat. Navuk 2 (1966) 121–123.Google Scholar