相关论文: MaxDim of some simple groups

We conclude from the results of Hanguang Meng and Xiuyun Guo some corollaries about the existence of strictly 2-maximal subgroups in groups. We give examples of groups that illustrate properties of strictly 2-maximal subgroups.

Artin-Tits groups act on a certain delta-hyperbolic complex, called the "additional length complex". For an element of the group, acting loxodromically on this complex is a property analogous to the property of being pseudo-Anosov for…

Real-world road networks have an approximate scale-invariance property; can one devise mathematical models of random networks whose distributions are {\em exactly} invariant under Euclidean scaling? This requires working in the continuum…

In this paper, we mainly elucidate a close relationship between the topological entropy and mean dimension theory for actions of polynomial growth groups. We show that metric mean dimension and mean Hausdorff dimension of subshifts with…

Thompson's group F is the group of all increasing dyadic piecewise linear homeomorphisms of the closed unit interval. We compute Sigma^m(F) and Sigma^m(F;Z), the homotopical and homological Bieri-Neumann-Strebel-Renz invariants of F, and we…

For every hyperbolic group and more general hyperbolic graphs, we construct an equivariant ideal bicombing: this is a homological analogue of the geodesic flow on negatively curved manifolds. We then construct a cohomological invariant…

The complexity of (unbounded-arity) Max-CSPs under structural restrictions is poorly understood. The two most general hypergraph properties known to ensure tractability of Max-CSPs, $\beta$-acyclicity and bounded (incidence) MIM-width, are…

The paper deals with quasigroups having a trivial group of automorphisms and a trivial group of autotopisms. Examples of such quasigroups and methods of their verification are given.

We study period growth in co-context-free groups, giving general results and looking at specific examples such as Thompson groups $T$ and $V$ and the Houghton groups $H_m$. Along the way, we give a refined upper bound on the word metric in…

Let K be a multiquadratic number field. We investigate the average dimension of 2-Selmer groups over K for the family of all elliptic curves over the rational numbers (ordered by height). We give upper and lower bounds for this average. In…

The goal of this article is to clarify the relationship between the topos of triads and the neo-Riemannian PLR-group. To do this, we first develop some theory of generalized interval systems: 1) we prove the well known fact that every pair…

We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the Mathieu sporadic group M12. As a consequence, we confirm for this group the Kimmerle's conjecture on prime graphs.

We present an infinite family of finite planar graphs $\{X_n\}$ with degree at most five and such that for some constant $c > 0$, $$ \lambda_1(X_n) \geq c(\frac{\log \diam(X_n)}{\diam(X_n)})^2\,, $$ where $\lambda_1$ denotes the smallest…

We investigate invariants for random elements of different hyperbolic groups. We provide a method, using Cayley graphs of groups, to compute the probability distribution of the minimal length of a random word, and explicitly compute the…

We analyze how the transient dynamics of large dynamical systems in the vicinity of a stationary point, modeled by a set of randomly coupled linear differential equations, depends on the network topology. We characterize the transient…

We systematically investigate cocycle superrigidity in the setting of finite rank median spaces for product groups and Kazhdan groups. By employing a dynamical approach to superrigidity, we establish, for a median space X of finite rank,…

The Matsushita fundamental groups of a graph $X$, denoted $\pi_1^r(X)$, are certain discrete versions of the fundamental group for topological spaces. For $r=2$, these groups have a nice combinatorial description, due to Sankar. In this…

We discuss the topology of the symmetry groups appearing in compactified (super-)gravity, and discuss two applications. First, we demonstrate that for 3 dimensional sigma models on a symmetric space G/H with G non-compact and H the maximal…

Let X be a smooth separated geometrically connected variety over F_q and f:Y-> X a smooth projective morphism. We compare the invariant dimensions of the l-adic representation V_l and the F_l-representation \bar V_l of the geometric \'etale…

In this paper, we determine the finite groups with a Sylow $r$-subgroup contained in a unique maximal subgroup. The proof involves a reduction to almost simple groups, and our main theorem extends earlier work of Aschbacher in the special…