相关论文: Maximal subgroups of SL(n, Z)

In this paper, the concept of a maximal L-subgroup of an L-group has been defined in the spirit of classical group theory. Then, a level subset characterization has been established for the same. Then, this notion of maximal L-subgroups has…

We study a particular class of representations from the fundamental groups of punctured spheres $\Sigma_{0,n}$ to the group $\text{PSL} (2,\mathbb R)$ (and their moduli spaces), that we call \emph{super-maximal}. Super-maximal…

For each finite classical group $G$, we classify the subgroups of $G$ which act transitively on a $G$-invariant set of subspaces of the natural module, where the subspaces are either totally isotropic or nondegenerate. Our proof uses the…

In this paper we classify all maximal subgroups M of a nearly simple primitive rank 3 group G of type L=Omega_{2m+1}(3), m > 3; acting on an L-orbit E of non-singular points of the natural module for L such that 1_P^G <=1_M^G where P is a…

We prove that non-trivial representations of the alternating group $A_n$ are reducible over a primitive proper subgroup which is isomorphic to some alternating group $A_m$.

We describe and count the maximal subsemigroups of many well-known monoids of transformations and monoids of partitions. More precisely, we find the maximal subsemigroups of the full spectrum of monoids of order- or orientation-preserving…

Ge asked the question whether $LF_{\infty}$ can be embedded into $LF_2$ as a maximal subfactor. We answer it affirmatively by three different approaches, all containing the same key ingredient: the existence of maximal subgroups with…

For $n\geq 1$, let $\rho_n$ denote the standard action of $GL_2(\Z)$ on the space $P_n(\Z)\simeq\Z^{n+1}$ of homogeneous polynomials of degree $n$ in two variables, with integer coefficients. For $G$ a non-amenable subgroup of $GL_2(\Z)$,…

We characterize the maximal discrete subgroups of $SO^+(2,n+2)$, which contain the discriminant kernel of an even lattice, which contains two hyperbolic planes over $\mathbb{Z}$. They coincide with the normalizers in $SO^+(2,n+2)$ and are…

Let $k$ be an arbitrary field. We classify the maximal reductive subgroups of maximal rank in any classical simple algebraic $k$-group in terms of combinatorial data associated to their indices. This result complements [S, 2022], which does…

We show that in the extended modular group PGL(2,Z) there are exactly seven finite subgroups up to conjugacy; three subgroups of size 2, one subgroup each of size 3, 4, and 6, and the trivial subgroup of size 1.

Let D be an infinite division ring, n a natural number and N a subnormal subgroup of GLn(D) such that n = 1 or the center of D contains at least five elements. This paper contains two main results. In the first one we prove that each…

It is proved that any infinite Abelian topological group of prime exponent has an infinite maximally almost periodic subgroup.

We propose graph theoretic equivalents for existence of a finite projective plane. We then develop a new approach and see that the problem of existence of a finite projective plane of order n is linked up with a subset of sharply 2…

We construct a sequence of primitive-stable representations of free groups into PSL(2,C) whose ranks go to infinity, but whose images are discrete with quotient manifolds that converge geometrically to a knot complement. In particular this…

Let $p$ be a prime number and suppose that every maximal subgroup of a finite group is either $p$-nilpotent or has prime index. Such group need not be $p$-solvable, and we study its structure by proving that only one nonabelian simple group…

Every synchronising permutation group is primitive and of one of three types: affine, almost simple, or diagonal. We exhibit the first known example of a synchronising diagonal type group. More precisely, we show that…

This paper is a survey on the works [MS77, MS79, MS81] on maximal subgroups in finitely generated linear groups, and the works that followed it [GG08, GG13b, GG13a, Kap03, Iva92, HO16, GM16, AGS14, Sf90, Sf98, Per05, AKT16, FG18, GS17]…

A subgroup of a finite group G is said to be second maximal if it is maximal in every maximal subgroup of G that contains it. A question which has received considerable attention asks: can every positive integer occur as the number of the…

We give here the exact maximal subgroup growth of two classes of polycyclic groups. Let $G_k = \langle x_1, x_2, ..., x_k \mid x_ix_jx_i^{-1}x_j \text{ for all } i < j \rangle$. So $G_k = \mathbb{Z} \rtimes (\mathbb{Z} \rtimes (\mathbb{Z}…