相关论文: Finiteness Conditions for the $n$-fold Tensor Prod…

Baer characterized capable finite abelian groups (a group is capable if it is isomorphic to the quotient of some group by its center) by a condition on the size of the factors in the invariant factor decomposition (the group must be…

Let $G$ be a group. We denote by $\nu(G)$ a certain extension of the non-abelian tensor square $[G,G^{\varphi}]$ by $G \times G$. We prove that if $G$ is a finite potent $p$-group, then $[G,G^{\varphi}]$ and the $k$-th term of the lower…

For every Lie group $G$, we compute the maximal $n$ such that an $n$-fold product of nonabelian free groups embeds into $G$.

It is proved that all finitely generated subgroups of generalized free product of two groups are finitely separable provided that free factors have this property and amalgamated subgroups are normal in corresponding factors and satisfy the…

We define an action of the braid group (associated with a simple Lie algebra) on the space of $n$-tuples of power series in an indeterminate u, with constant term zero. Using this, we give a sufficient condition for a tensor product of…

We provide new computations in bounded cohomology: A group is boundedly acyclic if its bounded cohomology with trivial real coefficients is zero in all positive degrees. We show that there exists a continuum of finitely generated…

A group is called $(m,n)$-bicyclic if it can be expressed as a product of two cyclic subgroups of orders $m$ and $n$, respectively. The classification and characterization of finite bicyclic groups have long been important problems in group…

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…

For all sufficiently large odd integers $n$, the following version of Higman's embedding theorem is proved in the variety ${\cal B}_n$ of all groups satisfying the identity $x^n=1$. A finitely generated group $G$ from ${\cal B}_n$ has a…

We show that for some absolute (explicit) constant $C$, the following holds for every finitely generated group $G$, and all $d >0$: If there is some $ R_0 > \exp(\exp(Cd^C))$ for which the number of elements in a ball of radius $R_0$ in a…

In this paper, we propose an axiomatic definition for a tensor product categorification. A tensor product categorification is an abelian category with a categorical action of a Kac-Moody algebra g in the sense of Rouquier or Khovanov-Lauda…

We prove that the category of $\mathbb{Z}_2 ^n$-manifolds has all finite products. Further, we show that a $\mathbb{Z}_2 ^n$-manifold (resp., a $\mathbb{Z}_2 ^n$-morphism) can be reconstructed from its algebra of global $\mathbb{Z}_2…

We prove several results detecting ciclicity or nilpotency of a finite group $G$ in terms of inequalities involving the orders of the elements of $G$ and the orders of the elements of the cyclic group of order $|G|$. We prove that, among…

Let G denote either a special orthogonal group or a symplectic group defined over the complex numbers. We prove the following saturation result for G: given dominant weights \lambda^1, ..., \lambda^r such that the tensor product…

In this paper, we introduce the relative $n$-tensor nilpotent degree of a finite group $G$ with respect to a subgroup $H$ of $G$. The aim of this paper is to investigate this concept and give some results on this topic.

In 1968, John Thompson proved that a finite group G is solvable if and only if every 2-generator subgroup of G is solvable. In this paper, we prove that solvability of a finite group G is guaranteed by a seemingly weaker condition: G is…

In this paper we show that for a torsion-free abelian group $G$, $\operatorname{rank}_\mathbb{Z}G<\infty$ if and only if there exists a Noetherian $G$-graded ring $R$ such that the set $\{R_g \neq 0\}$ generates the group $G$. For every $G$…

Recently, the authors gave some conditions under which a direct product of finitely many groups is $\mathcal{V}-$capable if and only if each of its factors is $\mathcal{V}-$capable for some varieties $\mathcal{V}$. In this paper, we extend…

Let $G$ be an $\ell$-group (which is short for ``lattice-ordered abelian group''). Baker and Beynon proved that $G$ is finitely presented iff it is finitely generated and projective. In the category $\mathcal U$ of {\it unital}…

Let $\Gamma$ be a finite group. Consider the wreath product $G_n := \Gamma^n \rtimes S_n$ and the subgroup $K_n := \Delta_n \times S_n\subseteq G_n$, where $S_n$ is the symmetric group and $\Delta_n$ is the diagonal subgroup of $\Gamma^n$.…