In this paper, we define the vanishing-off subgroup of a nonabelian group. We study the structure of the quotient of this subgroup and a central series obtained from this subgroup. MSC primary: 20C15, MSC secondary: 20D25

In finite group theory, one of the most influential ideas is the notion of Sylow p-subgroup. It was used to classify many groups of finite order. Despite original intentions to use it with finite group, it was extended to study Lie group, which inspires recent development in p-compact group. Here, we will discuss some aspects of Sylow’s Subgroup Theorem. In particular, the focus is on a finite ...

This is a short survey of the progress on the congruence subgroup problem since the sixties when the first major results on the integral unimodular groups appeared. It is aimed at the non-specialists and avoids technical details.