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Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions

Elena Fuchs, Chen Meiri, Peter Sarnak (2014)

Journal of the European Mathematical Society

We give a criterion which ensures that a group generated by Cartan involutions in the automorph group of a rational quadratic form of signature ( n - 1 , 1 ) is “thin”, namely it is of infinite index in the latter. It is based on a graph defined on the integral Cartan root vectors, as well as Vinberg’s theory of hyperbolic reflection groups. The criterion is shown to be robust for showing that many hyperbolic hypergeometric groups for n F n - 1 are thin.

Modules over group rings of soluble groups with a certain condition of maximality

Olga Dashkova (2011)

Open Mathematics

Let A be an R G-module, where R is an integral domain and G is a soluble group. Suppose that C G(A) = 1 and A/C A(G) is not a noetherian R-module. Let L nnd(G) be the family of all subgroups H of G such that A/C A(H) is not a noetherian R-module. In this paper we study the structure of those G for which L nnd(G) satisfies the maximal condition.

On groups of similitudes in associative rings

Evgenii L. Bashkirov (2008)

Commentationes Mathematicae Universitatis Carolinae

Let R be an associative ring with 1 and R × the multiplicative group of invertible elements of R . In the paper, subgroups of R × which may be regarded as analogues of the similitude group of a non-degenerate sesquilinear reflexive form and of the isometry group of such a form are defined in an abstract way. The main result states that a unipotent abstractly defined similitude must belong to the corresponding abstractly defined isometry group.

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