1. The centralizer of a maximal torus is called a Cartan subgroup. 2. The center is the centralizer of the entire ring " R ". 3. The double centralizer theorems give conditions under which one can conclude that equality occurs. 4. Making the extended centralizer of an element x equal to the normalizer of the set 5. For involutions or non-real elements, centralizer and extended centralizer are equal. 6. For involutions or non-real elements, centralizer and extended centralizer are equal. 7. He is a centralizer by instinct and a disperser by ( current ) intellectual conviction. 8. The extended centralizer of an element of a group G is always a subgroup of G. 9. Its centralizer has the form 2 12 : M 12 and has conjugates inside the monomial subgroup. 10. The centralizer of \ mathfrak { g } itself is called the center of \ mathfrak { g }.
