Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T19:40:33.220Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Isomorphisms Between Certain Congruence Groups, II

Published online by Cambridge University Press:  20 November 2018

Robert Solazzi
Robert Solazzi*
Affiliation:
Indiana University, Bloomington, Indiana
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For integral domains of characteristic not 2, we prove here that the symplectic and unitary congruence groups are not isomorphic if the Witt indices are at least 3. This is Theorem 2.1; Theorem 3.3 describes the isomorphisms of unitary congruence groups.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 5 , October 1973 , pp. 1006 - 1014
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Dieudonné, J., La géométrie des groupes classiques (Springer-Verlag, Berlin, 1963).Google Scholar
2. Dieudonné, J., On the automorphisms of the classical groups, Mem. Amer. Math. Soc, New York, 1951.Google Scholar
3. O'Meara, O. T., The automorphisms of the standard symplectic group over any integral domain, J. Reine Angew. Math. 230 (1968), 104–138.Google Scholar
4. O'Meara, O. T., Group theoretic characterization of transvections using CDC, Math. Z. 110 (1969), 385–394.Google Scholar
5. O'Meara, and Zassenhaus, , The automorphisms of the linear congruence groups over Dedekind domains, J. Number Theory 1 (1969), 211–221.Google Scholar
6. Rickart, C. E., Isomorphic groups of linear transformations, Amer. J. Math. 72 (1950), 451–464.Google Scholar
7. Rickart, C. E., Isomorphic groups of linear transformations, II, Amer. J. Math. 78 (1951), 697–716.Google Scholar
8. Solazzi, R. E., The automorphisms of certain subgroups of PGLn(V), Illinois J. Math. 16 (1972), 330–349.Google Scholar
9. Solazzi, R. E., The automorphisms of the symplectic congruence groups, J. Algebra 21 (1972), 91–102.Google Scholar
10. Solazzi, R. E., Isomorphism theory of congruence groups, Bull. Amer. Math. Soc. 77 (1971), 164–168.Google Scholar
11. Solazzi, R. E., On the isomorphism between certain congruence groups, Proc. Amer. Math. Soc. 35 (1972), 405–410.Google Scholar