What Group Contains Elements a and b in Abstract Algebra?

In summary, abstract algebra is a branch of mathematics that studies algebraic structures and their operations. It has practical applications in fields such as physics, engineering, and computer science, and provides a foundation for more advanced areas of mathematics. Some key concepts in abstract algebra include group theory, ring theory, field theory, and module theory. It differs from traditional algebra by focusing on algebraic structures rather than specific numerical values. Common applications of abstract algebra include coding theory, cryptography, and studying symmetries in physics.
  • #1
ShengyaoLiang
23
0
1)
find a group that contains elements a and b such that ︱a︱=︱b︱= 2 and

a) ︱ab︱ = 3 b) ︱ab︱=4 c) ︱ab︱=5

2)
suppose that H is a proper subgroup of Z under addition and H contains 18, 30 and 40.
determine H?


does anyone can help me out?
and ...i am really in hurry...thanks...

besides...i need all the steps...
 
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  • #2
can somebody help me out?

especially the second question...
 
  • #3
What have you tried? Have you had any thoughts at all on these problems?
 

1. What is abstract algebra?

Abstract algebra is a branch of mathematics that studies algebraic structures such as groups, rings, and fields. It is concerned with studying the properties and relationships between these structures and their operations.

2. Why is abstract algebra important?

Abstract algebra has many practical applications in fields such as physics, engineering, and computer science. It also provides a foundation for more advanced areas of mathematics such as number theory and topology.

3. What are some key concepts in abstract algebra?

Some key concepts in abstract algebra include group theory, ring theory, field theory, and module theory. Other important concepts include homomorphisms, isomorphisms, and substructures.

4. How is abstract algebra different from traditional algebra?

Abstract algebra is more general and abstract compared to traditional algebra, which focuses on solving equations with known variables. Abstract algebra deals with algebraic structures and their properties, rather than specific numerical values.

5. What are some common applications of abstract algebra?

Abstract algebra has many applications in fields such as coding theory, cryptography, and computer science. It is also used in physics to study symmetries and in chemistry to understand molecular structures. Additionally, abstract algebra has applications in economic and social sciences, such as game theory and voting systems.

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