Jordan Regular Generators of General Linear Groups


  • Lucknow University, Department of Mathematics and Astronomy, Lucknow, 226007, India
  • Indian Institute of Technology, Department of Mathematics, Delhi, 110016, India


In this article Jordan regular units have been introduced. In particular, it is proved that for n ≥ 2, the general linear group GL(2; F2n) can be generated by Jordan regular units. Further, presentations of GL(2, F4); GL(2, F8); GL(2, F16) and GL(2, F32) have been obtained having Jordan regular units as generators.


Jordan Regular Units, General Linear Groups

Subject Discipline

Mathematical Sciences

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A. Karrass, D. Solitar and W. Magnus, Combinatorial Group Theory, Dover Publications, INC, 1975.

G. Chiaselotti, Some presentations for the special linear groups on finite fields, Ann. Mat. Pura Appl., 180(2001), 359-372.

H. S. M. Coxeter and W. O. J. Mosser, Generators and Relations for Discrete Groups, Springer-Verlag, 1980.

Joseph J. Rotman, An Introduction to the theory of groups, fourth ed., Graduate Texts in Mathematics, vol. 148, Springer-Verlag, New York, 1995.

Michio Suzuki, Group Theory vol.1 , Gendai Sugaku [Modern Mathematics], vol.18, Iwanami Shoten, Tokyo, 1977.

Parvesh Kumari, R. K. Sharma and Meena Sahai, Jordan Regular Units in Rings and Group Rings, Pre-Print.

Pramod Kanwar, R. K. Sharma and Pooja Yadav, Lie Regular Generators of General Linear Groups II, International Electronic Journal of Algebra, 13, (2013), 91-108.

R. K. Sharma, Pooja Yadav and Pramod Kanwar, Lie Regular Generators of General Linear Groups, Comm. Algebra, 40(4) (2012), 1304-1315.

T. A. Francis, Presentations of the special and general linear groups, J. Algebra, 169(1994), 943-964.

The GAP groups, GAP-Groups, Algorithms and Programming, Version 4.4,2004, (


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