Parabolic subgroups in FC-type Artin groups

Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results of Cumplido, Gebhardt, Gonzales-Meneses and Wiest, known only for parabolic subgroups of finite type Artin groups, to parabolic subgroups of FC-type Artin groups. We show that the class of finite type parabolic subgroups is closed under intersection. We also study an analog of the curve complex for mapping class group constructed by Cumplido et al. using parabolic subgroups. We extend the construction of this complex, called the complex of parabolic subgroups, to FC-type Artin groups. We show that this simplicial complex is, in most cases, infinite diameter and conjecture that it is δ-hyperbolic.     

Maximal Subrings and Covering Numbers of Finite Semisimple Rings

We classify the maximal subrings of the ring of n×n matrices over a finite field, and show that these subrings may be divided into three types. We also describe all of the maximal subrings of a finite semisimple ring, and categorize them into two classes. As an application of these results, we calculate the covering number of a finite semisimple ring.     

有限CN-p-群

每个子群都C-正规的有限群称为CN-群.本文首先给出二元生成的CN-p-群的完全分类.在此基础上得到CN-p-群的结构:当p为奇素数时,有限群G为CNp-群当且仅当G的每个元都平凡地作用在Φ(G)上;有限群G为CN-2-群当且仅当对任意给定的a∈G,都有对任意g∈Φ(G),g~a=g或者对任意g∈Φ(G),g~a=g~(-1).最后给出两个CN-p-群的直积是CN-p-群的判定条件.     

Weighted estimates for the multilinear maximal function on the upper half‐spaces

For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates.     

Synthesis,Characterization, and Symmetry Relations of the Crystal Structures of Some Bis(dioxane) Adducts of Group 1 / Group 13 Heterometallic Trifluoroacetates

Four bis(dioxane) adducts of mixed‐metal trifluoroacetates, M[M′(O₂CCF₃)₄(C₄H₈O₂)₂] (M = Na, K, Cs, M′ = In and M = Cs, M′ = Ga) were synthesized by reaction of alkali metal trifluoroacetate and group 13 element trifluoroacetate in 1,4‐dioxane and completely characterized including X‐ray structure determination. Geometric parameters, empirical bond valences and frequencies of the symmetric C=O stretching vibrations show that the moisture sensitive solids are composed of dimeric structural moieties with site symmetry 1 , containing alkali metal ions and bis(dioxane)tetrakis(trifluoroacetato)indate or ‐gallate ions. The dimeric units are further connected by weaker “intermolecular” dioxane interactions to neighboring alkali metal ions. Closer inspection of space group symmetry, unit cell parameters and atom sites allows to rationalize the compounds as members of two isotypic pairs that are further closely related due to the group‐subgroup relation of their monoclinc space groups to a common orthorhombic supergroup.