Related papers: Krull dimension for limit groups IV: Adjoining roo…

In this paper, we introduce the concept of graded extension dimension for a group graded ring R, denoted by gr.ext.dim(R). We prove that when R is strongly graded, its graded extension dimension coincides with the non-graded extension…

In this paper we look at the automorphisms of the multiplicative group of finite nearfields. We find partial results for the actual automorphism groups. We find counting techniques for the size of all finite nearfields. We then show that…

EI categories can be thought of as amalgams of finite posets and finite groups and therefore the associated algebras are built up from incidence algebras and group algebras of finite groups. For this particular class of algebras we present…

Let $G$ be a finite group and let $cd(G)$ be the set of all irreducible complex character degrees of $G$. It was conjectured by Huppert in Illinois J. Math. 44 (2000) that, for every non-abelian finite simple group $H$, if $cd(G)=cd(H)$…

In this paper, we construct a family of reductive groups, including all reductive groups up to a given rank. We also construct a similar versal family of quasi-split reductive groups. This result generalizes a former result of N.Avni and…

The aim of this paper is to provide a new characterization of isomorphism classes of generalized Alexander quandles in terms of the underlying groups and their automorphisms. This extends the previous result [4, Theorem 1.4]. Additionally,…

We study the second cohomology group with coefficients in the adjoint module for a class of solvable Lie algebras $\mathcal{R}_{\mathcal{T}}$ that arise as maximal solvable extensions of nilpotent Lie algebras $\mathcal{N}$ of maximal rank.…

A disjoint $(v,k,k-1)$ difference family in an additive group $G$ is a partition of $G\setminus\{0\}$ into sets of size $k$ whose lists of differences cover, altogether, every non-zero element of $G$ exactly $k-1$ times. The main purpose of…

We construct an explicit filtration of the ring of algebraic power series by finite dimensional constructible sets, measuring the complexity of these series. As an application, we give a bound on the dimension of the set of algebraic power…

This work concerns in part the construction of conformal Jordan cells of infinite rank and their reductions to conformal Jordan cells of finite rank. It is also discussed how a procedure similar to Lie algebra contractions may reduce a…

We study the complexity of the isomorphism relation for various classes of closed subgroups of the group of permutations of the natural numbers. We use the setting of Borel reducibility between equivalence relations on Polish spaces. For…

In this paper, we give a survey of the known results concerning the tensor rank of the multiplication in finite extensions of finite fields, enriched with some not published recent results as well as analyzes enhancing the qualitative…

We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.

We study the return probability of finitely generated metabelian groups. We give a characterization of metabelian groups whose return probability is equivalent to $\exp(-n^\frac1{3} )$ in purely algebraic terms, namely the Krull dimension…

We extend Gromov's notion of asymptotic dimension of finitely generated groups to all discrete groups. In particular, we extend the Hurewicz type theorem proven in [B-D2] to general groups. Then we use this extension to prove a formula for…

Root subgroup factorization is a refinement of triangular (or LDU) factorization. For a complex reductive Lie group, and a choice of reduced factorization of the longest Weyl group element, the forward map from root subgroup coordinates to…

This is the third one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with orthogonal groups in odd dimension.

We give a method to construct new self-adjoint representations of the braid group. In particular, we give a family of irreducible self-adjoint representations of dimension arbitrarily large. Moreover we give sufficient conditions for a…

This chapter surveys recent and less recent results on convergence of Kleinian representations, following Thurston's Double Limit and "AH(acylindrical) is compact" Theorems.

This paper studies extension groups between certain Weyl modules for the algebraic group GL_n over the integers. Main results include: (1) A complete determination of Ext groups between Weyl modules whose highest weights differ by a single…