无限亚局部循环群及其自同构群

Automorphism groups of infinite meta-(locally cyclic) groups

作为之前工作的继续,本文研究了无限亚局部循环群的结构以及它们的自同构和自同构群.设A,B分别是秩1的无挠Abel群,G为n阶循环群.群E是A被G的扩张,G被A的扩张或者A被B的扩张.讨论了群E的结构以及它们的自同构,并得到了它们的自同构群.

As a continuation of previous work,in this paper,we mainly study the infinite meta-（locally cyclic） groups and their automorphism groups. Let A and B be torsion free abelian groups of rank 1,G be a cyclic group of order n,and let E be extensions of A by G,G by A or A by B respectively. We study the group structure of E as well as their automorphisms,especially their automorphism groups will be given.