Group theory, a cornerstone of modern algebra, provides a framework to explore the structure, symmetry, and internal operations of sets endowed with a binary operation. Central to this discipline is ...

In this paper, we find some connections between submodules of a module over a group ring RG and subgroups of a group G. Also, we prove that there is a direct connection between conjugate elements of G ...

Fusion systems have emerged as a powerful conceptual framework that encapsulates the conjugation relationships among p-subgroups of finite groups. This categorical approach not only unifies aspects of ...

We develop a Sylow theory for stable groups satisfying certain additional conditions (2-finiteness, solvability or smallness) and show that their maximal p-subgroups are locally finite and conjugate.