I am having dificulties with subgroups and how to develop generators.

I have a question

Find the numbers of generatos os a cyclic groups of orders Z6, Z8, Z12 and Z60

Printable View

- Dec 5th 2009, 04:02 PMrupecee1abstract algebra
I am having dificulties with subgroups and how to develop generators.

I have a question

Find the numbers of generatos os a cyclic groups of orders Z6, Z8, Z12 and Z60 - Dec 5th 2009, 04:07 PMlvleph
This is the wrong section.. Also, you may want to clarify your question a bit. I understand that you want $\displaystyle <x>$ for some group where $\displaystyle o(x)$ is one of the following $\displaystyle \{6,8,12,60\}$. But you never gave the group.

- Dec 5th 2009, 04:31 PMTheEmptySet
Cyclic groups of finite order are always isomorphic to the integers mod n

under addition.

Here is a link to the wiki on cyclic groups

Cyclic group - Wikipedia, the free encyclopedia

Note that cyclic groups always have $\displaystyle \varphi(n)$ generators where $\displaystyle \varphi$ is the Euler Phi function

Euler's totient function - Wikipedia, the free encyclopedia