 Gilman–Griess theorem

The Gilman–Griess theorem is a result in the field of group theory, specifically concerning the classification of finite simple groups. It characterizes certain groups that arise from group extensions. More specifically, the theorem provides a criterion for distinguishing between different types of groups based on the existence of certain properties in their subgroup structure. While the theorem is notable for providing insights into the structure of finite groups, it is particularly significant in the study of maximal subgroups and their interactions within simple groups.