On the isomorphisms between certain congruence groups

Solazzi, Robert E.

doi:10.1090/S0002-9939-1972-0308293-9

On the isomorphisms between certain congruence groups
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Proc. Amer. Math. Soc. 35 (1972), 405-410 Request permission

Abstract:

In this paper we study the possible isomorphisms between the congruence subgroups of the classical groups over integral domains by applying the involution-free techniques previously used by O’Meara and the author. We prove, in dimensions at least 6 and characteristic not 2, that a linear congruence group is never isomorphic to a symplectic congruence group nor to an isotropic unitary congruence group whose associated hermitian space has Witt index at least 3.

References

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Jean Dieudonné, La géométrie des groupes classiques, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963 (French). Seconde édition, revue et corrigée. MR 0158011

On the automorphisms of the classical groups

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