Completely decomposable direct summands of torsion--free abelian groups of finite rank

Multiplication Groups of Abelian Torsion-Free Groups of Finite Rank

For an Abelian group $G$, any homomorphism $μ\colon G\otimes G\rightarrow G$ is called a \textsf{multiplication} on $G$. The set $\text{Mult}\,G$ of all multiplications on an Abelian group $G$ itself is an Abelian group with respect to addition; the group is called the \textsf{multiplication group} of $G$. Let $\mathcal{A}_0$ be the class of all reduced block-rigid almost completely decomposable groups of ring type with cyclic regulator quotient. In this paper, for groups $G\in \mathcal{A}_0$, we describe groups $\text{Mult}\,G$. We prove that for $G\in \mathcal{A}_0$, the group $\text{Mult}\,…

带循环边群的自由群图的虚拟同调挠

Virtual homological torsion in graphs of free groups with cyclic edge groups

本文证明带循环边群的自由群图的双曲群，除非是自由群与曲面群的自由积，其有限指数子群的阿贝尔化包含任意有限阿贝尔群作为直和项，并由此推出自由积的 profinite 刚性及部分曲面词由词测度决定。

Bassian-有限阿贝尔群

Bassian-Finite Abelian Groups

引入严格位于co-Hopfian群与Dedekind-finite群之间的Bassian-finite阿贝尔群新类，证明其在挠群情况下与co-Hopficity等价，并构造了无挠非co-Hopfian及非Bassian-finite的Dedekind-finite群实例。

半广义Bassian群

Semi-Generalized Bassian Groups

本研究提出半广义Bassian群这一真广义Bassian群的非平凡推广概念，刻画了其在p-挠群、无挠群与分裂混合群情形下的结构，并分类了子群均在直和项中本质的相关群类。

图辫群同调中所有有限阶挠元

Torsion of every finite order in the homology of graph braid groups

本文确定了图辫群同调中所有有限阶挠元的结构，给出了显式代表元、最小图条件及无挠性判定，并证明了奇挠元首次出现的具体位置。

On Fox and augmentation quotients of semidirect products

Let $G$ be a group which is the semidirect product of a normal subgroup $N$ and some subgroup $T$. Let $I^n(G)$, $n\ge 1$, denote the powers of the augmentation ideal $I(G)$ of the group ring $\Z(G)$. Using homological methods the groups $Q_n(G,H) = I^{n-1}(G)I(H)/I^{n}(G)I(H)$, $H=G,N,T$, are functorially expressed in terms of enveloping algebras of certain Lie rings associated with $N$ and $T$, in the following cases: for $n\le 4$ and arbitrary $G,N,T$ (except from one direct summand of $Q_4(G,N)$), and for all $n\ge 2$ if certain filtration quotients of $N$ and $T$ are torsionfree.

co-Hopfian阿贝尔群的两个推广

Two Generalizations of co-Hopfian Abelian Groups

本文定义了广义co-Hopfian群和相对co-Hopfian群两类，完全刻画了p-群、无挠群及混合群的相应性质，并证明相对co-Hopfian p-群恰为co-Hopfian群，且两类遗传群在秩意义下重合。

The Roquette category of finite p-groups

Let p be a prime number. This paper introduces the Roquette category R_p of finite p-groups, which is an additive tensor category containing all finite p-groups among its objects. In R_p, every finite p-group P admits a canonical direct summand, called the edge of P. Moreover P splits uniquely as a direct sum of edges of Roquette p-groups, and the tensor structure of R_p can be described in terms of such edges. The main motivation for considering this category is that the additive functors from R_p to abelian groups are exactly the rational p-biset functors. This yields in particular very effi…