Related papers: JSJ Decompositions of pro-p Groups

In this short note we give a characterization of ZM-groups that uses the functions defined and studied in [3,4]. This leads to a proof of Conjecture 6 in [4].

I will survey some results in the theory of modular representations of a reductive $p$-adic group, in positive characteristic $\ell \neq p$ and $\ell=p$.

A JSJ decomposition of a group is a splitting that allows one to classify all possible splittings of the group over a certain family of edge groups. Although JSJ decompositions are not unique in general, Guirardel--Levitt have constructed a…

In this article, we introduce the notion of representations of polyadic groups and we investigate the connection between these representations and those of retract groups and covering groups.

We prove the conjugacy of Sylow $p$-subgroups of linear pseudofinite groups under the assumption of the existence of a finite Sylow $p$-subgroup. We also give an example of a linear pseudofinite group with non-conjugate Sylow $2$-subgroups.

Recently there has been a lot of research and progress in profinite groups. We survey some of the new results and discuss open problems. A central theme is decompositions of finite groups into bounded products of subsets of various kinds…

We provide a short and self-contained argument for the existence of Cartan-Iwahori-Matsumoto decompositions for reductive groups.

We define a local Sylow subgroup of a totally disconnected, locally compact group G to be a maximal pro-p subgroup of an open compact subgroup of G. We use these subgroups to define the p-localisation of G, a locally virtually pro-p group…

We give a complete characterization of torsion-free hyperbolic groups which are homogeneous in the sense of first-order logic, in terms of the JSJ decompositions of their free factors.

We present an application of Hodge theory towards the study of irreducible unitary representations of reductive Lie groups. We describe a conjecture about such representations and discuss some progress towards its proof.

We determine a strong form of the decomposition theorem for proper toric maps over finite fields.

Pairwise non-isomorphic semigroups obtained from the finite inverse symmetric semigroup $\mathcal{IS}_n ,$ finite symmetric semigroup $\mathcal{T}_n$ and bicyclic semigroup by the deformed multiplication proposed by Ljapin are classified.

Recall that a $p$-group of order $p^ {n} >p^ {3} $ is of maximal class, if its nilpotency class is $n-1$. In this paper, we study the $p$-groups of maximal class. Furthermore, we introduce a subgroup of a $p$-group of maximal class called…

We give a group theoretic proof of the splitting of sharply 2-transitive groups of characteristic 3.

The structure of finite and locally finite groups in which every element has prime power order (CP-groups) is well known. In this paper we note that the combination of our earlier results with the available information on the structure of…

In this paper we construct compact forms associated with a complex Lie supergroup with Lie superalgebra of classical type.

In this paper, the notion of pronormal L-subgroups of an L-group has been introduced by using the concept of conjugate L-subgroup. The notion of pronormal L-subgroups has been investigated in context of normality and subnormality of…

An algebraic deformation theory of dialgebra morphisms is obtained.

We give a survey of recent developments in the investigation of the various local-global conjectures for representations of finite groups.

We formulate and prove relative versions of several classical decompositions known in the theory of Chevalley groups over commutative rings. As an application we obtain upper estimates for the width of principal congruence subgroups in…