The intersection of subgroups refers to the set of elements that are common to two or more subgroups within a group. This concept is essential in understanding the structure of groups and their subgroups, as it leads to important properties such as normality and the formation of new subgroups. In the context of group theory, particularly when discussing Sylow theorems, the intersection can help identify Sylow subgroups and their relationships with one another, which is crucial for analyzing group structures.
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