论文标题
II组的积分
Integrals of groups II
论文作者
论文摘要
$ g $的$积分$是$ h $的commutator子群的组$ h $。本文继续研究ARXIV工作：1803.10179的群体积分的调查。我们学习： （1）足够的条件，可以在有限的集成基团的积分范围内绑定，并使组成为可集成的必要条件。 （2）存在着Abelian $ p $ - 群体的$ P $ - 组和所有Abelian群体的Nilpotent积分的存在。 （3）（有限或无限）阿贝尔组的积分，包括尼尔植物积分，某些积分，周期性组，无扭转组和有限生成的组中有有限索引的组。 （4）来自给定品种的组的各种积分，各种可集成的组和积分（当存在的何时）仍然属于这样的类别的群体。 （5）针对有限生成的无中心群体的集成能的积分和对整合性的表征。 （6）笛卡尔产品的积分，然后将其用于构建无贴岩积分的可集成涂鸦基团的示例。 我们以许多开放的问题结束了论文。
An $integral$ of a group $G$ is a group $H$ whose commutator subgroup is isomorphic to $G$. This paper continues the investigation on integrals of groups started in the work arXiv:1803.10179. We study: (1) A sufficient condition for a bound on the order of an integral for a finite integrable group and a necessary condition for a group to be integrable. (2) The existence of integrals that are $p$-groups for abelian $p$-groups, and of nilpotent integrals for all abelian groups. (3) Integrals of (finite or infinite) abelian groups, including nilpotent integrals, groups with finite index in some integral, periodic groups, torsion-free groups and finitely generated groups. (4) The variety of integrals of groups from a given variety, varieties of integrable groups and classes of groups whose integrals (when they exist) still belong to such a class. (5) Integrals of profinite groups and a characterization for integrability for finitely generated profinite centreless groups. (6) Integrals of Cartesian products, which are then used to construct examples of integrable profinite groups without a profinite integral. We end the paper with a number of open problems.
