VeeEight said:Looks good to me.
e = abab implies
b = ababb = aba which implies
ba = abaa = ab
halvizo1031 said:Thanks! Is there another way i can show this?
Dick said:Why do you need another way? What did you have in mind?
halvizo1031 said:well i just don't want to have the same answer as someone else.
Dick said:It's a simple problem. There's a simple answer. There's a few different permutations on the expression of that answer, but they are all really the same. Wouldn't it be better to move on to the next problem?
halvizo1031 said:That's true. I'm having trouble showing that an element k is a generator of Zn if and only if k and n are relatively prime.
Dick said:The order 2 part of the problem has nothing to do with proving k is a generator of Zn if k and n are relatively prime. Try thinking about them independently.
A group whose elements have order 2 refers to a mathematical structure where all the elements in the group have a specific property called "order 2". This means that when an element is multiplied by itself, the result is the identity element of the group.
The order of an element in a group whose elements have order 2 is equal to 2. This is because the element multiplied by itself will always result in the identity element, and no other power of the element will do the same.
Yes, a group can have elements with different orders. However, if all the elements in a group have order 2, then the group is called a "group of order 2".
Elements with order 2 play an important role in the structure and properties of a group. They can help identify the center of a group and can also be used to classify groups into different types, such as abelian or non-abelian.
Groups whose elements have order 2 have various applications in fields such as physics, chemistry, and computer science. For example, they are used in quantum mechanics to represent spin states of particles, in chemistry to describe molecular symmetry, and in computer science for error correction codes and cryptography.