Related papers: Adequate Subgroups II
The notion of adequate subgroups was introduced by Jack Thorne [42]. It is a weakening of the notion of big subgroups used in generalizations of the Taylor-Wiles method for proving the automorphy of certain Galois representations. Using…
The notion of adequate subgroups was introduced by Jack Thorne [59]. It is a weakening of the notion of big subgroups used by Wiles and Taylor in proving automorphy lifting theorems for certain Galois representations. Using this idea,…
We study adequate subgroups of $GL_n$ over a finite field. This notion is useful in the study of automorphy lifting theorems. In particular, we give a sufficient condition for a subgroup to be adequate.
Thorne introduced the notion of adequate representations as a weakening of the big representations used by Wiles and Taylor and others. In this appendix to Dieulefait's paper, Automorphy of Symm5(GL(2)) and base change, we show that certain…
Recently, we have endowed various categories of groups with topologies. The purpose of this paper is to introduce on these categories others topologies which are statistically more suitable to study well-known problems in groups theory. We…
The main purpose of this article is to initiate a systematic study of Semihypergroups, first introduced by C. Dunkl [4], I. Jewett [13] and R. Spector [20] independently around 1972. We introduce and study several natural algebraic and…
The concepts of the scale and tidy subgroups for an automorphism of a totally disconnected locally compact group were defined in seminal work by George A. Willis in the 1990s, and recently generalized to the case of endomorphisms (G. A.…
The concept of an adequate transversal of an abundant semigroup was introduced by El-Qallali in [8] whilst in [7], he and Fountain initiated the study of quasi-adequate semigroups as natural generalisations of orthodox semigroups. In this…
We construct a local deformation problem for residual Galois representations $\bar{\rho}$ valued in an arbitrary reductive group $\hat{G}$ which we use to develop a variant of the Taylor-Wiles method. Our generalization allows Taylor-Wiles…
The concept of hypergroup is generalization of group, first was introduced by Marty [9]. This theory had applications to several domains. Marty had applied them to groups, algebraic functions and rational functions. M. Krasner has studied…
A new notion of independence relation is given and associated to it, the class of flat theories, a subclass of strong stable theories including the superstable ones is introduced. More precisely, after introducing this independence…
We call a finite group G ultrasolvable if it has a characteristic subgroup series whose factors are cyclic. It was shown by Durbin--McDonald that the automorphism group of an ultrasolvable group is supersolvable. The converse statement was…
Extending the Wedderburn-Artin theory of (classically) semisimple associative rings to the realm of topological rings with right linear topology, we show that the abelian category of left contramodules over such a ring is split…
Good semigroups form a class of submonoids of $\mathbb{N}^d$ containing the value semigroups of curve singularities. In this article, we describe a partition of the complements of good semigroup ideals, having as main application the…
The notion of almost centralizer and almost commutator are introduced and basic properties are established. They are used to study $\widetilde{\mathfrak M}\_c$-groups, i. e.groups for which every descending chain of centralizers each having…
Rosenmann and Ventura asked "What is the right definition of dependence of subgroups for general groups?". Here we aim to answer this question. We consider a definition of subgroup independence which is a special case of a…
In this article, we introduce an interesting topology-like concept concerning groups (and with almost the same method it can be defined for other algebraic systems). Given an arbitrary group $G$, we define a {\em topo-system} on $G$ as a…
Value semigroups of non irreducible singular algebraic curves and their fractional ideals are submonoids of $\mathbb Z^n$ that are closed under infimums, have a conductor and fulfill a special compatibility property on their elements.…
A discrete subset $S$ of a topological group $G$ is called a {\it suitable set} for $G$ if $S\cup \{e\}$ is closed in $G$ and the subgroup generated by $S$ is dense in $G$, where $e$ is the identity element of $G$. In this paper, the…
Let G be a group, and H a G-group defined by an imbedding map $G\rightarrow H$; in [12] we have defined a topology on a subset of normal subgroups of $H$, the so-called prime ideals. In this work, we generalize this topology to other…