Group homomorphisms between cyclic groups (1 Viewer)

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Describe al group homomorphisms [tex] \phi [/tex] : [tex] C_4 [/tex] --> [tex] C_6 [/tex]

The book I study from seems to pass over Group Homomorphisms very fast. So I decided to look at Artin's to help and it uses the same definition. So I think I am just not digesting something I should be. I know it's defined as [tex]\phi[/tex] (a*b) = [tex]\phi[/tex] (a) * [tex]\phi[/tex] and that it maps the inverses to the inverses but I just have no idea how to apply these.
I forgot a b in the definition of phi(a*b) = phi(a)*phi(b)


Homework Helper
If you specify [itex]\phi(1)[/itex], then what does this say about the value of [itex]\phi[/itex] at the other elements in C_4? Also, a general fact about homomorphisms is that the order of [itex]\phi(g)[/itex] must divide the order of g. Can you prove this? By the way, you can edit posts.

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving