A stabilizer in group theory is a subgroup that consists of all the elements of a group that fix a particular point under a group action. This concept is essential when analyzing how groups operate on sets, as it helps to understand the structure of orbits and the behavior of specific elements within those orbits. Additionally, in the context of regular representations, stabilizers help describe how the group elements interact with their representations, revealing important information about the overall structure and properties of the group.
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