Visual Group Theory, Lecture 3.6: Normalizers скачать в хорошем качестве

Visual Group Theory, Lecture 3.6: Normalizers

Visual Group Theory, Lecture 3.6: Normalizers A subgroup H of G is normal if xH=Hx for all x in G. If H is not normal, then the normalizer is the set of elements for which xH=Hx. Obviously, the normalizer has to be at least H and at most G, and so in some sense, this is measuring "how close H is to being normal". We interpret this in terms of Cayley diagrams, and then prove some basic properties of normalizers: they are always subgroups, and they are unions of cosets -- precisely, those left cosets that are also right cosets. Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/...