Related papers: On the Sylow Theorem for Skew Braces

We prove the equivalence between the simplicial Orlicz cohomology and the Orlicz-de Rham cohomology in the case of Lie groups. Since the first one is a quasi-isometry invariant for uniformly contractible simplicial complexes with bounded…

In this paper, we show that each finite group $G$ containing at most $p^2$ Sylow $p$-subgroups for each odd prime number $p$, is a solvable group. In fact, we give a positive answer to the conjecture in \cite{Rob}.

Using the theory of perverse sheaves of vanishing cycles, we define a homological invariant of knots in three-manifolds, similar to the three-manifold invariant constructed by Abouzaid and the second author. We use spaces of SL(2,C) flat…

We prove local limit theorems for a cocycle over a semiflow by establishing topological, mixing properties of the associated skew product semiflow. We also establish conditional rational weak mixing of certain skew product semiflows and…

We prove the following higher-order Szego theorems: if a measure on the unit circle has absolutely continuous part $w(\theta)$ and Verblunsky coefficients $\alpha$ with square-summable variation, then for any positive integer $m$, $\int…

We prove a Berger-type theorem which asserts that if the orthogonal subgroup generated by the torsion tensor (pulled back to a point by parallel transport) of a metric connection with skew-symmetric torsion is not transitive on the sphere,…

Let $H\leq K$ be subgroups of a group G. We say that H is strongly closed in K with respect to G if whenever $a^g \in K$ where $a \in H, g \in G,$ then $a^g \in H.$ In this paper, we investigate the structure of a group G under the…

We present a different version of the well-known connection between Hopf--Galois structures and skew braces, building on a recent paper of A. Koch and P. J. Truman. We show that the known results that involve this connection easily carry…

In the present paper we generalize the notion of a Heyting algebra to the non-commutative setting and hence introduce what we believe to be the proper notion of the implication in skew lattices. We list several examples of skew Heyting…

This is an expository paper for Chapter 6 of Proper and Improper Forcing. Now includes an exposition of Shelah's proof of preservation of Sacks property as well as omega-omega bounding.

We prove two gluing theorems for special Lagrangian (SL) conifolds in complex space C^m. Conifolds are a key ingredient in the compactification problem for moduli spaces of compact SLs in Calabi-Yau manifolds. In particular, our theorems…

One of the central tools in the classification of simple algebraic groups is the distinction between semisimple subgroups and unipotent subgroups. It is not a priori clear how to make this distinction for torsion-free subgroups of a group…

In this paper we begin the study of set-theoretic type solution of the braid equation. Our theory includes set-theoretical solutions as basic examples. We show that the relationships between set-theoretical solutions, q-cycle sets,…

We prove that if R is a left Noetherian and left regular ring then the same is true for any bijective skew PBW extension A of R. From this we get Serre's Theorem for such extensions. We show that skew PBW extensions and its localizations…

In Part I of this paper, we introduced a class of certain algebras of finite dimension over a field. All these algebras are split, symmetric and local. Here we continue to investigate their Loewy structure. We show that in many cases their…

We define a solvable extension of the graph 2-step nilpotent Lie algebras of [5] by adding elements corresponding to the 3-cliques of the graph. We study some of their basic properties and we prove that two such Lie algebras are isomorphic…

We prove a prime decomposition theorem for string links in a thickened surface. Namely, we prove that any non-braid string link $\ell \subset \Sigma \times I$, where $\Sigma$ is a compact orientable (not necessarily closed) surface other…

We prove twisted homological stability with polynomial coefficients for automorphism groups of free nilpotent groups of any given class. These groups interpolate between two extremes for which homological stability was known before, the…

A finitely presented group is semistable at infinity if all proper rays in the Cayley 2-complex are properly homotopic. A long standing open question asks whether all finitely presented groups are semistable at infinity. This article…

Suppose that Y is a cyclic cover of projective space branched over a hyperplane arrangement D, and that U is the complement of the ramification locus in Y. The first theorem implies that the Beilinson-Hodge conjecture holds for U if certain…