Maximal Subgroup - Maximal Normal Subgroup

Maximal Normal Subgroup

Similarly, a normal subgroup N of G is said to be a maximal normal subgroup (or maximal proper normal subgroup) of G if N

Theorem: A normal subgroup N of a group G is a maximal normal subgroup if and only if the quotient G/N is simple.

Read more about this topic:  Maximal Subgroup

Famous quotes containing the word normal:

    You know that fiction, prose rather, is possibly the roughest trade of all in writing. You do not have the reference, the old important reference. You have the sheet of blank paper, the pencil, and the obligation to invent truer than things can be true. You have to take what is not palpable and make it completely palpable and also have it seem normal and so that it can become a part of experience of the person who reads it.
    Ernest Hemingway (1899–1961)