Visual Group Theory, Lecture 5.6: The Sylow theorems

Описание к видео Visual Group Theory, Lecture 5.6: The Sylow theorems

Visual Group Theory, Lecture 5.6: The Sylow theorems

The three Sylow theorems help us understand the structure of non-abelian groups by placing strong restrictions on their p-subgroups (i.e., subgroups of prime power order). The first Sylow theorem says that for every p^k dividing |G|=p^n*m, there is a p-subgroup of that order, and unless k=n, it is nested in a larger p-subgroup. The second Sylow theorem says that all maximal p-subgroups are conjugate. The third Sylow theorem says the the number of maximal p-subgroups divides m, and is congruent to 1 modulo p.

Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/...

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