Sylow Subgroup6

Exhibit two Sylow 2-subgroups of Symmetric group $S_5$
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.5 Exercise 4.5.8 Solution: ...
Exhibit all of the Sylow 2-subgroups of Symmetric group $S_4$
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.5 Exercise 4.5.7 Solution: ...
For odd primes $p$, the Sylow $p$-subgroups of Diherdral group are cyclic and normal
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.5 Exercise 4.5.5 Solution: ...
In a finite group, conjugation permutes sub-Sylow subgroups
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.5 Exercise 4.5.2 Solution: ...
Sylow subgroups of a finite group which are contained in some other subgroup are also Sylow there
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.5 Exercise 4.5.1 Solution: ...
Interaction of Sylow subgroups with quotients
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.3 Exercise 3.3.9 Let $p$ be...