Direct Product30

Compute all Sylow subgroups of Dihedral group $D_{12}$ and $S_3\times S_3$
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.5 Exercise 4.5.1 Solution: ...
Use direct products to construct groups with some given properties
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.18 Solution:...
Basic properties of n-ary direct products of groups
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.16 Solution:...
Definition of the n-ary direct product of groups
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.15 Solution:...
A quotient by a product is isomorphic to the product of quotients
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.14 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: ...
In the direct product of the quaternion group and an elementary abelian 2-group, all subgroups are normal
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.6 Solution: ...
The direct product of groups with no nonnormal subgroups may have nonnormal subgroups
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.5 Solution: ...
The Sylow numbers of a direct product are products of the Sylow numbers
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.4 Solution: ...