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Let $Σ$ be a compact connected oriented surface with one boundary component, and let $π$ be the fundamental group of $Σ$ . The Johnson filtration is a decreasing sequence of subgroups of the Torelli group of $Σ$ , whose $k$ -th term consists of the self-homeomorphisms of $Σ$ that act trivially at the level of the $k$ -th nilpotent quotient of $π$ . Morita defined a homomorphism from the $k$ -th term of the Johnson filtration to the third homology group of the $k$ -th nilpotent quotient of $π$ . In this paper, we replace groups...

Irréductibilité générique des produits tensoriels de monodromies

Ivan Marin (2004)

Bulletin de la Société Mathématique de France

Nous étudions le problème de l’irréductibilité du produit tensoriel de deux représentations irréductibles d’un groupe fondamental $G = π_{1} (X)$ , quand $X$ est le complémentaire d’hypersurfaces dans un espace projectif. Nous mettons en place un formalisme adapté et utilisons une approche par monodromie pour définir une classe de représentations irréductibles de $G$ dont les produits tensoriels restent irréductibles pour des valeurs génériques de paramètres de définition. Ceci est appliqué au groupe de tresses pures...

Lower central series, augmentation quotients and homology of groups.

Luzius Grünenfelder (1980)

Commentarii mathematici Helvetici

Mild 2-relator pro- $p$ -groups.

Bush, Michael R., Gärtner, Jochen, Labute, John, Vogel, Denis (2011)

The New York Journal of Mathematics [electronic only]

More on five commutator identities.

Donadze, G., Ladra, M. (2007)

Journal of Homotopy and Related Structures

Nonassociative algebras: some applications.

Santos González, Consuelo Martínez (2003)

Revista Matemática Iberoamericana

Nonassociative algebras can be applied, either directly or using their particular methods, to many other branches of Mathematics and other Sciences. Here emphasis will be given to two concrete applications of nonassociative algebras. In the first one, an application to group theory in the line of the Restricted Burnside Problem will be considered. The second one opens a door to some applications of non-associative algebras to Error correcting Codes and Cryptography.

Normally constrained $p$ -groups

C. Bonmassar, C. M. Scoppola (1999)

Bollettino dell'Unione Matematica Italiana

In questo lavoro si studiano i gruppi finiti di ordine una potenza di un numero primo in cui i sottogruppi normali sono compresi tra due termini successivi della serie centrale discendente. Si ottengono numerose proprietà generali di questi gruppi, e una loro dettagliata descrizione in classe di nilpotenza 2.

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