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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the isomorphisms between certain congruence groups


Author: Robert E. Solazzi
Journal: Proc. Amer. Math. Soc. 35 (1972), 405-410
MSC: Primary 20H15
DOI: https://doi.org/10.1090/S0002-9939-1972-0308293-9
MathSciNet review: 0308293
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0308293-9
Keywords: Classical group, centralizer, skew-hermitian form, linear, symplectic, unitary congruence group, transvection, isomorphism
Article copyright: © Copyright 1972 American Mathematical Society

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