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Discussiones Mathematicae General Algebra and Applications 20(2) (2000) 159-167
DOI: https://doi.org/10.7151/dmgaa.1013

A FACTORIZATION OF ELEMENTS IN PSL(2,F), WHERE F =Q, R

Jan Ambrosiewicz

Institute of Mathematics, Technical University of Białystok
15-351 Białystok, ul. Wiejska 45A, Poland

Abstract

Let G be a group and K_n = {g ∈ G:o(g) = n}. It is prowed: (i) if F = R, n > 4, then PSL(2, F) = K_n²; (ii) if F = Q, R, n = ∞, then PSL(2, F) = K_n²; (iii) if F = R, then PSL(2, F) = K₃³; (iv) if F = Q, R, then PSL(2, F) = K₂³∪E, E ∉ K₂³, where E denotes the unit matrix; (v) if F = Q, then PSL(2, F) ≠ K₃³.

Keywords: factorization of linear groups, linear groups, matrix representations of groups, sets of elements of the same order in groups.

1991 Mathematics Subject Classification: 20G20, 11E57, 15A23, 20G15.

References

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[6]	J. Ambrosiewicz, Square of set of elements of order two in orthogonal groups, Publ. Math. Debrecen 41 (1992), 189-198.
[7]	J. Ambrosiewicz, If K is a real field then cn(PSL(2,K)) = 4, Demonstratio Math. 29 (1996), 783-785.
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[9]	E.W. Ellers, R. Frank, and W. Nolte, Bireflectionality of the weak orthogonal and the weak sympletic groups, J. Algebra 88 (1984), 63-67.

Received 15 January 1997
Revised 12 July 1999
Revised 15 November 1999