论文标题
简单群体的扭转方面
Torsion aspects of varieties of simplicial groups
论文作者
论文摘要
简单组中有一个扭转理论的晶格，因此，具有截短的摩尔复合物在一定程度以下/高于截短的摩尔复合物中给出了无扭转/无扭转类别。我们研究了这些扭转理论对简单群体的某些子类别的限制。特别是，我们证明了D.Conduché的2条划线模块的类别和Ashley的跨组成部分是半亚伯利亚人，我们对它们的扭转理论进行了一些描述。这些扭转理论的例子还引起了曲奇尼和菲诺基氏梭菌的新示例，以及无扭转理论（TTF理论）的例子。
There is a lattice of torsion theories in simplicial groups such that the torsion/torsion-free categories are given by simplicial groups with truncated Moore complex below/above a certain degree. We study the restriction of these torsion theories to certain subcategories of simplicial groups. In particular, we prove that the categories of D.Conduché's 2-crossed modules and Ashley's crossed complexes in groups are semi-abelian and we give some descriptions of their torsion theories. These examples of torsion theories also give rise to new examples of pretorsion theories in the sense of A. Facchini and C. Finocchiaro, as well as examples of torsion torsion-free theories (TTF theories).
