What are the elements of each order in D_n+Z_9 for n = 7 and 11?

In summary, abstract algebra is a branch of mathematics that studies the abstract properties of algebraic structures such as groups, rings, fields, and vector spaces. It has many real-world applications in fields such as cryptography, coding theory, computer science, and physics. The key concepts in abstract algebra include groups, rings, fields, vector spaces, and homomorphisms, and to improve understanding, it is important to have a strong foundation in algebra, number theory, and linear algebra, and to practice solving problems and seeking additional resources. There are also common misconceptions that abstract algebra is only for advanced mathematicians and only involves manipulating symbols, when in fact it involves critical thinking and problem-solving.
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ccrfan44
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Pick a number n which is the product of 2 distinct primes 5 or more. Find the number of elements of each order in the groupd D(sub)n+Z(sub)9, completely explaining your work. Verify that these number add up to the order of the group.

Ive used 7 and 11 as my primes. So now do I use these primes in D_n since to where i get D_7+Z_9 and D_11+Z_9? This is where I am confused.
 
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Also once i have that info, then where do i go from here?
 

What is abstract algebra?

Abstract algebra is a branch of mathematics that studies algebraic structures such as groups, rings, fields, and vector spaces. It focuses on the abstract properties of these structures rather than specific numbers or equations.

What are some real-world applications of abstract algebra?

Abstract algebra has many applications in various fields such as cryptography, coding theory, computer science, and physics. For example, group theory is used in chemistry to study symmetries of molecules, while ring theory is used in coding theory to design error-correcting codes.

What are the key concepts in abstract algebra?

The key concepts in abstract algebra include groups, rings, fields, vector spaces, and homomorphisms. These concepts are used to study the properties and relationships of algebraic structures, and to solve problems in various applications.

How can I improve my understanding of abstract algebra?

To improve your understanding of abstract algebra, it is important to have a strong foundation in algebra, number theory, and linear algebra. It is also helpful to practice solving problems and working through proofs, and to seek out additional resources such as textbooks, online courses, and study groups.

Are there any common misconceptions about abstract algebra?

One common misconception about abstract algebra is that it is only for advanced mathematicians. In reality, abstract algebra is a fundamental subject that can be studied at various levels and has many practical applications. Another misconception is that abstract algebra is only about manipulating symbols, when in fact it involves critical thinking, problem-solving, and creative reasoning.

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