Involutions and commutators in orthogonal groups

Journal of the Australian Mathematical Society

Volumn 65, Issue 1, 1998, Pages 1-36

  Knüppel, Frieder ^a   Thomsen, Gerd ^a  

^a Math Seminar   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040689717     PISSN: 14467887     EISSN: None     Source Type: Journal    
DOI: 10.1017/s1446788700039379     Document Type: Article

References (22)

1. F. Bünger, F. Knüppel and K. Nielsen, 'Products of symmetries in unitary groups', Linear Algebra Appl. 260 (1997), 9-42.
2. n(v) as products of commutators of symmetries', Manuscript, Notre Dame, September 1994.
3. J. Hahn and O. T. O'Meara, The classical groups and K-theory (Springer, Berlin, 1989).
4. B. Huppert, 'Isometrien von Vektorräumen I', Arch. Math. 35 (1980), 164-176.
5. _, 'Isometrien von Vektorräumen II', Math. Z. 175 (1980), 5-20.
6. _, Angewandte lineare Algebra (de Gruyter, Berlin, 1990).
7. n (n ≥ 5)', Math. Japon. 2 (1951), 59-60.
8. F. Knüppel, 'Products of involutions in orthogonal groups', Ann. Discrete Math. 37 (1988), 231-248.
9. _, 'Products of simple isometries of given conjugacy types', Forum Math. 5 (1993), 441-458.
10. F. Knüppel and K. Nielsen, 'On products of two involutions in the orthogonal group of a vector space', Linear Algebra Appl. 94 (1987), 209-216.
11. _, 'SL(V) is 4-reflectional', Geom. Dedicata 38 (1991), 301-308.
12. F. Lorenz, Quadratische Formen über Körpern, Lecture Notes in Math. 130 (Springer, Berlin, 1970).
13. K. Nielsen, 'Conjugacy classes and commutators in symplectic groups', to appear.
14. O. Ore, 'Some remarks on commutators', Proc. Amer. Math. Soc. 2 (1951), 307-314.
15. J.-M. Quin, 'On commutators in orthogonal groups', Chinese J. Math. 5 (1965), 437-449.
16. P. Scherk, 'On the decomposition of orthogonalities into symmetries', Proc. Amer. Math. Soc. 1 (1950), 481-491.
17. R. C. Thompson, 'Commutators in the special and general linear groups', Trans. Amer. Math. Soc. 1 (1950), 481-491.
18. G. Thomsen Läangenprobleme in klassischen Gruppen. Teil I: Involutionen mit zwei-dimensionalem Negativraum als Erzeugende der speziellen linearen Gruppe. Teil II: Die Kommutatorgruppe der orthogonalen Gruppe und der Kern der Spinornorm (Dissertation, Kiel, 1991).
19. H. Tôyama, 'On commutators of matrices', Kodai Math. Sem. Rep. 5-6 (1949), 1-2.
20. G. E. Wall, 'On the conjugacy classes in the unitary, symplectic and orthogonal groups', J. Austral. Math. Soc. 3 (1963), 1-62.
21. M. J. Wonenburger, 'Transformations which are products of two involutions', J. Math. Mech. 16 (1966), 327-338.
22. H. Zassenhaus. 'On the spinor norm', Arch. Math. 13 (1962), 434-451.