Abstract algebra question?

In summary, abstract algebra is a branch of mathematics that studies algebraic structures such as groups, rings, and fields. It differs from other branches of mathematics by focusing on abstract concepts and structures, rather than specific numbers and equations. Some examples of abstract algebraic structures include groups, rings, fields, vector spaces, and algebras. This field has many applications in various fields such as computer science, physics, engineering, and cryptography. The basic operations in abstract algebra are addition, subtraction, multiplication, and division, but they are defined differently depending on the algebraic structure being studied. Abstract algebra allows for the generalization of concepts and the exploration of new structures, making it a fundamental and versatile branch of mathematics.
  • #1
NateDoris
1
0
abstract algebra question??

here is the problem from abstract algebra, anyone could help? Thanks a lot!

let G be a finite group. Show that in the disjoint cycle form of the right regular representation Tg(x)=xg of G each cycle has length | g |.
(Tg(x) means T sub g of x)

loofinf forward seeing some answers! Thanks!
 
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  • #2


What have you tried so far? There's a reason why this forum asks people to use a standard form for posting homework questions.

From what you've posted, it's not obvious whether you even understand the definitions involved.
 

1. What is abstract algebra?

Abstract algebra is a branch of mathematics that studies algebraic structures such as groups, rings, and fields. Unlike elementary algebra, which deals with specific numbers and equations, abstract algebra focuses on the properties and relationships between these algebraic structures.

2. What are some examples of abstract algebraic structures?

Some examples of abstract algebraic structures include groups, rings, fields, vector spaces, and algebras.

3. What are the main applications of abstract algebra?

Abstract algebra has many applications in various fields such as computer science, physics, engineering, and cryptography. It is also used to study symmetries and patterns in nature, and to solve problems in number theory and geometry.

4. What are the basic operations in abstract algebra?

The basic operations in abstract algebra are addition, subtraction, multiplication, and division. However, these operations are defined differently depending on the algebraic structure being studied. For example, in a group, the operation of addition may represent the combining of two elements, while in a ring, it may represent the operation of multiplication.

5. How does abstract algebra differ from other branches of mathematics?

Abstract algebra differs from other branches of mathematics in that it deals with abstract concepts and structures, rather than specific numbers and equations. It also focuses on the properties and relationships between these structures, rather than computations and solutions. Additionally, abstract algebra allows for the generalization of concepts and the exploration of new structures, making it a fundamental and versatile branch of mathematics.

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