The main goal of this work is to examine classes of finite groups in which normality, permutability and Sylow-permutability are transitive relations. These classes of groups are called T , PT and PST , respectively. The main focus is on direct products of T , PT and PST groups and the behavior of a collection of cyclic normal, permutable and Sylow-permutable subgroups under the intersection map. In general, a direct product of finitely many groups from one of these classes does not belong to the same class, unless the orders of the direct factors are relatively prime. Examples suggest that for solvable groups it is not required to have relatively prime orders to stay in the class. In addition, the concept of normal, permutable and S-permutable cyclic sensitivity is tied with that of Tc, PTc and PSTc groups, in which cyclic subnormal subgroups are normal, permutable or Sylow-permutable. In the process another way of looking at the Dedekind, Iwasawa and nilpotent groups is provided as well as possible interplay between direct products and the intersection map is observed.

A group G is called a barely transitive group if it acts transitively and faithfully on an infinite set and every orbit of every proper subgroup is finite. A subgroup H of a group G is called a permutable subgroup, if H commutes with every subgroup of G. We showed that if an infinitely generated barely transitive group G has a permutable point stabilizer, then G is locally finite. We proved that if a barely transitive group G has an abelian point stabilizer H, then G is isomorphic to one of the followings: (i) G is a metabelian locally finite p-group, (ii) G is a finitely generated quasi-finite group (in particular H is finite), (iii) G is a finitely generated group with a maximal normal subgroup N where N is a locally finite metabelian group. In particular, G=N is a quasi-finite simple group. In all of the three cases, G is periodic.

Families of operators that are triangularizable must necessarily satisfy a number of spectral mapping properties. These necessary conditions are often sufficient as well. This thesis investigates such properties in finite dimensional and infinite dimensional Banach spaces. In addition, we investigate whether approximate spectral mapping conditions (being "close" in some sense) is similarly a sufficient condition.

Families of operators that are triangularizable must necessarily satisfy a number of spectral mapping properties. These necessary conditions are often sufficient as well. This thesis investigates such properties in finite dimensional and infinite dimensional Banach spaces. In addition, we investigate whether approximate spectral mapping conditions (being "close" in some sense) is similarly a sufficient condition.

For $n\geq2$, a variety $\mathcal{V}$ is said to be congruence $n$-permutable if every algebra $\mathbf{A}\in\mathcal{V}$ satisfies $\alpha\circ^n\beta=\beta\circ^n\alpha$, for all $\alpha,\beta\in \Con(\mathbf{A})$. Furthermore, given any algebra $\mathbf{A}$ and $k\geq1$, a $k$-dimensional Hagemann relation on $\mathbf{A}$ is a reflexive compatible relation $R\subseteq A\times A$ such that $R^{-1}\not\subseteq R\circ^k R$. A famous result of J. Hagemann and A. Mitschke shows that a variety $\mathcal{V}$ is congruence $n$-permutable if and only if $\mathcal{V}$ has no member carrying an $(n-1)$-dimensional Hagemann relation: by using this criterion, we provide another Maltsev characterization of congruence $n$-permutability, equivalent to the well-known Schmidt's and Hagemann-Mitschke's (\cite{HagMit}) term-based descriptions. We further establish that the omission by varieties of certain special configurations of Hagemann relations induces the satisfaction of suitable Maltsev conditions. These omission properties may be used to characterize congruence $n$-permutable idempotent varieties for some $n\geq2$, congruence 2-permutable idempotent varieties and congruence 3-permutable locally finite idempotent varieties, yielding that the following are prime Maltsev conditions: \begin{enumerate} \item congruence $n$-permutability for some $n\geq2$ with respect to idempotent varieties; \item congruence 2-permutability with respect to idempotent varieties; \item congruence 3-permutability with respect to locally finite idempotent varieties. \end{enumerate} Finally, we focus on the analysis of a family of strong Maltsev conditions, which we denote by $\{\mathcal{D}_n:2\leq n<\omega\}$, such that any variety $\mathcal{V}$ is congruence $n$-permutable whenever $\mathcal{D}_n$ is interpretable in $\mathcal{V}$. Among various other properties, we also show that the $\mathcal{D}_n$'s with odd $n\geq3$ generate decomposable strong Maltsev filters in the lattice of interpretability types. / Thesis / Doctor of Philosophy (PhD)

Cette thèse représente une étude d'un nouvel indicateur d'aide à la décision pour le problème d'ordonnancement d'ateliers de production sous présence d'incertitudes. Les contributions apportées dans ce travail se situent dans le contexte des groupes d'opérations permutables. Cette approche consiste à proposer une solution d'ordonnancement flexible caractérisant un ensemble fini non-énuméré d'ordonnancements. Un opérateur est ensuite censé sélectionner l'ordonnancement qui répond le mieux aux perturbations survenues dans l'atelier. Nous nous intéressons plus particulièrement à cette phase de sélection et nous mettons l'accent sur l’intérêt de l'humain pour la prise de décision. Dans un premier temps, nous présentons le meilleur des cas; indicateur d'aide à la décision pour le calcul du meilleur ordonnancement caractérisé par l'ordonnancement de groupes. Nous proposons des bornes inférieures pour le calcul des dates de début/fin des opérations. Ces bornes sont ensuite implémentées dans une méthode de séparation et d'évaluation permettant le calculer du meilleur des cas. Grâce à des simulations effectuées sur des instances de job shop de la littérature, nous mettons l'accent sur l'utilité et la performance d'un tel indicateur dans un système d'aide à la décision. Enfin, nous proposons une Interface Homme-Machine (IHM) adaptée à l'ordonnancement de groupes et pilotée par un système d'aide à la décision multicritères. L'implémentation de cette IHM sur un cas d'étude réel a permis de soulever certaines pratiques efficaces pour l'aide à la décision dans le contexte de l'ordonnancement sous incertitudes. / This thesis represents a study of a new decision-aid criterion for manufacturing scheduling under uncertainties. The contributions made in this work relate to the groups of permutable operations context. This approach consists of proposing a flexible scheduling solution characterizing a non-enumerated and finite set of schedules. An operator is then supposed to select the appropriate schedule that best copes with the disturbances occurred on the shop floor. We focus particularly on this selection phase and we emphasize the important of the human for decision making. First, we present the best-case; a decision-aid criterion for computing the best schedule characterized by the groups of permutable operations method. We propose lower bounds for computing the best starting/completion time of operations. These lower bounds are then implemented in a branch and bound procedure in order to compute the best-case. Through to several simulations carried out on literature benchmark instances, we stress the usefulness of such criterion in a decision-aid system. Finally, we propose a Human-Machine-Interface (HMI) adapted to the groups of permutable operations and driven by a multi-criteria decision-aid system. The implementation results of this HMI on a real case study provided some insight about the practice of decision-making and scheduling under uncertainties.