Permutation11

Classify groups of order 6
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.2 Exercise 4.2.10 Solution:...
Subgroups of finite index force the existence of normal subgroups of bounded index
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.2 Exercise 4.2.8 Solution: ...
The quaternion group is not a subgroup of Symmetric group for any n less than 8
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.2 Exercise 4.2.7 Solution: ...
Compute a permutation representation of Dihedral group of order 8
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.2 Exercise 4.2.6 Solution: ...
Compute permutation representations of Dihedral group of order 8
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.2 Exercise 4.2.5 Solution: ...
Symmetric group acts on the n-fold direct product of a group by permuting the factors
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.8 Solution: ...
Finite direct products are isomorphic up to permutation of the factors
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.7 Solution: ...
Compute the orbits, cycle decompositions, and stabilizers of some given group actions of Sym(3)
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.1 Exercise 4.1.4 Let $S_3$ ...
A group action is faithful precisely when the kernel of the corresponding permutation representation is trivial
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.7 Exercise 1.7.6 Prove that...
The kernel of a group action is precisely the kernel of the induced permutation representation
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.7 Exercise 1.7.5 Prove that...