SA Subgroup
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, in the realm of group theory, a subgroup of a group is termed a SA subgroup if the centralizer of any nonidentity element in the subgroup is precisely the subgroup. Equivalently, an SA subgroup is a centrally closed abelian subgroup. SA subgroups were introduced in finite groups theory for the classification of finite simple groups. Some important results about them: Any SA subgroup is a maximal abelian subgroup, that is, it is not properly contained i...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, in the realm of group theory, a subgroup of a group is termed a SA subgroup if the centralizer of any nonidentity element in the subgroup is precisely the subgroup. Equivalently, an SA subgroup is a centrally closed abelian subgroup. SA subgroups were introduced in finite groups theory for the classification of finite simple groups. Some important results about them: Any SA subgroup is a maximal abelian subgroup, that is, it is not properly contained in another abelian subgroup. For a CA group, the SA subgroups are precisely the maximal abelian subgroups. SA subgroups are known for certain characters associated with them termed exceptional characters.
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