Need Help with Graduate Algebra Problems?

In summary, the conversation is about a person asking for help with learning Modern algebra and finding solutions to problems in a specific textbook. The rules of the forum prohibit giving complete solutions to problems, but users can provide guidance and direction if the person shows effort in solving the problem.
  • #1
mthhtm33
1
0
I am trying to learn Modern algebra on my own and am having some difficulties without having a solution manual handy. I am studying Algebra by Larry C. Grove. I'd like to post problems and if anyone can provide solutions, that would be greatly appreciated!

1) If x and y are commuting elements in a group G, show |xy| divides LCM (|x|,|y|); equality holds if <x> intersect <y> = 1.

2) If P is a p-Sylow subgroup of G, show that Ng(Ng(P)) = Ng(P).

Thanks!
 
Physics news on Phys.org
  • #2
The rules of this forum prohibit giving solutions to problems (see Rules).
On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.​

If you show what you have tried, though, there are quite a few people who can steer you in the right direction.
 

FAQ: Need Help with Graduate Algebra Problems?

What is graduate algebra?

Graduate algebra is a branch of mathematics that deals with the study of algebraic structures, such as groups, rings, and fields, at an advanced level. It typically involves abstract concepts and proofs, rather than concrete applications.

What topics are typically covered in graduate algebra courses?

Topics covered in graduate algebra courses may include group theory, ring theory, field theory, Galois theory, homological algebra, and commutative algebra. These topics build upon the basic concepts of algebra learned in undergraduate courses and delve deeper into the theory and applications.

What are some common applications of graduate algebra?

Graduate algebra has many applications in various fields such as physics, computer science, and cryptography. It is also used in other branches of mathematics, including number theory, geometry, and topology. Some specific applications include error-correcting codes, public-key cryptography, and symmetry in physics.

What makes solving graduate algebra problems challenging?

Graduate algebra problems can be challenging because they require a strong understanding of abstract concepts and the ability to think critically and creatively. The problems often involve complex mathematical structures and require advanced techniques and proofs to solve.

How can I improve my skills in solving graduate algebra problems?

Practice, patience, and persistence are key to improving one's skills in solving graduate algebra problems. It is also helpful to study the underlying concepts and theories, and to work through examples and practice problems. Seeking help from professors, classmates, or online resources can also be beneficial.

Similar threads

Help with a Linear Algebra problem please
Replies
3
Views
1K
No group of order 10,000 is simple
Replies
1
Views
1K
Direct Proof that every zero of p(T) is an eigenvalue of T
Replies
24
Views
2K
A detail in a proof about isomorphism classes of groups of order 21
Replies
5
Views
2K
Proof that Algebraic Integers Form a Subring
Replies
1
Views
2K
MHB Show that the groups are abelian
Replies
1
Views
1K
[Linear Algebra] Show that H ∩ K is a subspace of V
Replies
5
Views
6K
Limit problem involving two circles and a line
Replies
8
Views
1K
Subnormal p-Sylow Subgroup of Finite Group
Replies
9
Views
2K
Lagrange multipliers understanding
Replies
8
Views
1K

Hot Threads

Recent Insights

Back
Top