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Complète réductibilité

Jean-Pierre Serre (2003/2004)

Séminaire Bourbaki

La notion de complète réductibilité d’une représentation linéaire $Γ \to {𝐆𝐋}_{n}$ peut se définir en termes de l’action de $Γ$ sur l’immeuble de Tits de ${𝐆𝐋}_{n}$ . Cela suggère une notion analogue pour tous les immeubles sphériques, et donc aussi pour tous les groupes réductifs. On verra comment cette notion se traduit en termes topologiques et quelles applications on peut en tirer.

Completely 0-simple semigroups and their associated graphs and groups.

C.H. Houghton (1977)

Semigroup forum

Completely decomposable abelian groups any pure subgroup of which is completely decomposable

Ladislav Bican (1974)

Czechoslovak Mathematical Journal

Completely decomposable abelian groups any regular subgroup of which is completely decomposable

Ladislav Bican (1975)

Czechoslovak Mathematical Journal

Completely decomposable pure subgroups of completely decomposable abelian groups

L. Fuchs, G. Viljoen (1994)

Rendiconti del Seminario Matematico della Università di Padova

Completely dissociative groupoids

Milton Braitt, David Hobby, Donald Silberger (2012)

Mathematica Bohemica

In a groupoid, consider arbitrarily parenthesized expressions on the $k$ variables $x_{0}, x_{1}, \dots x_{k - 1}$ where each $x_{i}$ appears once and all variables appear in order of their indices. We call these expressions $k$ -ary formal products, and denote the set containing all of them by $F^{σ} (k)$ . If $u, v \in F^{σ} (k)$ are distinct, the statement that $u$ and $v$ are equal for all values of $x_{0}, x_{1}, \dots x_{k - 1}$ is a generalized associative law. Among other results, we show that many small groupoids are completely dissociative, meaning that no generalized associative law holds...