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The Connes-Kasparov conjecture for almost connected groups and for linear p -adic groups

Jérôme Chabert, Siegfried Echterhoff, Ryszard Nest (2003)

Publications Mathématiques de l'IHÉS

Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C*-algebra of G is an isomorphism. The same is shown for the groups of k-rational points of any linear algebraic group over a local field k of characteristic zero.

The converse of Schur's Lemma in group rings

M. Alaoui, A. Haily (2006)

Publicacions Matemàtiques

In this paper, we study the structure of group rings by means of endomorphism rings of their modules. The main tools used here, are the subrings fixed by automorphisms and the converse of Schur's lemma. Some results are obtained on fixed subrings and on primary decomposition of group rings.

The covariety of perfect numerical semigroups with fixed Frobenius number

María Ángeles Moreno-Frías, José Carlos Rosales (2024)

Czechoslovak Mathematical Journal

Let S be a numerical semigroup. We say that h S is an isolated gap of S if { h - 1 , h + 1 } S . A numerical semigroup without isolated gaps is called a perfect numerical semigroup. Denote by m ( S ) the multiplicity of a numerical semigroup S . A covariety is a nonempty family 𝒞 of numerical semigroups that fulfills the following conditions: there exists the minimum of 𝒞 , the intersection of two elements of 𝒞 is again an element of 𝒞 , and S { m ( S ) } 𝒞 for all S 𝒞 such that S min ( 𝒞 ) . We prove that the set 𝒫 ( F ) = { S : S is a perfect numerical semigroup with...

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