SA subgroup

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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.