Finding Generators for Groups: A Guide

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In summary, Euler's totient function can determine the number of elements in a group, specifically the invertible elements of \mathbb{Z}_n. However, finding generators for such groups can be difficult and it may be helpful to consult other resources or use a Cayley table.
  • #1
cragar
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Homework Statement


Does Euler's totient function tell me how many elements are in my group?

And once I know how many elements are in my group. the generators are the ones that are relatively prime with the number of element in my group.
Are my statements correct.
 
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  • #2
cragar said:

Homework Statement


Does Euler's totient function tell me how many elements are in my group?

And once I know how many elements are in my group. the generators are the ones that are relatively prime with the number of element in my group.
Are my statements correct.

Could you please clarify a bit? What group exactly are you talking about? Are you talking about the invertible elements of [itex]\mathbb{Z}_n[/itex]??
 
  • #3
I am talking about the elements in Z(star)n . so the elements in my group have no common factors other than 1 with n,
 
  • #4
Yes, the number of elements in 2n is indeed phi(n). With phi the Euler totient function.
But your statement of the generators is not true. It's very difficult to find generators for such a groups...
 
  • #5
thanks for your help, my book is not very clear on how to find generators. Should I try to read another book on finding generators or make a Cayley table.
 

1. What is a group in science?

A group in science refers to a collection of individuals or objects that share certain characteristics or properties. It can also refer to a group of scientists working together on a specific research project.

2. How are groups formed in science?

Groups in science can be formed in various ways, such as through random selection, based on specific criteria or characteristics, or through self-selection by individuals with similar interests or expertise.

3. What is the purpose of forming groups in scientific research?

The purpose of forming groups in scientific research is to facilitate collaboration, share resources and expertise, and increase the efficiency and accuracy of research studies by pooling together different perspectives and skills.

4. What are some examples of groups in science?

Some examples of groups in science include research teams, scientific societies, academic departments, and international collaborations.

5. What are some challenges in working with groups in scientific research?

Some challenges in working with groups in scientific research include communication issues, conflicting ideas or approaches, and difficulties in coordinating tasks and schedules.

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