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
From playlist Visual Group Theory
Simple Group 168 - Sylow Theory - Part 1
Abstract Algebra: Let G be a simple group of order 168. We calculate the number of Sylow subgroups, number of elements of a given order, and conjugacy class structure. In Part 1, we consider Sylow-p subgroup for p = 3, 7.
From playlist Abstract Algebra
Group theory 14: Sylow theorems
This lecture is part of an online mathematics course on group theory. It gives the proofs of the Sylow theorems about the Sylow p-subgroups: those of order the largest power of p dividing the order of a group. Correction: Yenan Wang pointed out that at 18:18 D4 should be D8, the dihedral
From playlist Group theory
Simple Group 168 - Sylow Theory - Part 2
Note: Part 5 goes off the rails; I can't just assume the subgroup we choose normalizes H_2 a priori. We can still fix with elementary methods and the occasional lucky break. Fix for Part 5 (2:15) - disregard table: Key to note is that there are no elements of orders 6, 14, or 21 (s
From playlist Abstract Algebra
GT20. Overview of Sylow Theory
Abstract Algebra: As an analogue of Cauchy's Theorem for subgroups, we state the three Sylow Theorems for finite groups. Examples include S3 and A4. We also note the analogue to Sylow Theory for p-groups. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-gr
From playlist Abstract Algebra
AKPotW: Normalizer of a p-Sylow Subgroup [Algebra]
A neat result about the normalizer of a p-sylow subgroup. For a written solution, check out the blog!
From playlist Center of Math: Problems of the Week
Sylow Theory for Order 12 Groups 1
Abstract Algebra: Let G be a finite group of order 12. We apply Sylow theory to study such groups. In Part 1, we consider the abelian cases and A4, the alternating group on 4 letters.
From playlist Abstract Algebra
In this tutorial we define a subgroup and prove two theorem that help us identify a subgroup. These proofs are simple to understand. There are also two examples of subgroups.
From playlist Abstract algebra
Sylow Theory for Order 12 Groups 2
Abstract Algebra: Let G be a finite group of order 12. Using Sylow Theory, we consider the isomorphism types of G when n_3 = 1 and n_1. In this case, G is isomorphic to either D_12, the symmetry group of a regular hexagon, or a nontrivial semidirect product of Z/3 and Z/4.
From playlist Abstract Algebra
Group theory 15:Groups of order 12
This lecture is part of an online mathematics course on group theory. It uses the Sylow theorems to classify the groups of order 12, and finds their subgroups.
From playlist Group theory
GT20.1. Sylow Theorems - Proofs
Abstract Algebra: We give proofs of the three Sylow Theorems. Techniques include the class equation and group actions on subgroups. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-theory Master list at http://mathdoctorbob.org/UReddit.html
From playlist Abstract Algebra
GT20.2 Sylow Theory for Simple 60
EDIT: At 6:50, 1, 3, 5, 7 should be 1, 3, 7, 9. At 9:35, n3 should be n2. Abstract Algebra: Using Sylow theory, we show that any simple, non-abelian group with 60 elements is isomorphic to A_5, the alternating group on 5 letters. As an application, we show that A_5 is isomorphic to t
From playlist Abstract Algebra
Definition of a Subgroup in Abstract Algebra with Examples of Subgroups
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Subgroup in Abstract Algebra with Examples of Subgroups
From playlist Abstract Algebra