Can an element of a quotient group G/N in an isomorphism f:G/N--H map back onto itself if it does not have a corresponding element in H? The example I am looking at is the quotient group of the group of symmetries of an n-gon, G, where n is an even number and N equal to the normal subgroup...
eok20 is right. That did blow my head up when I read it. But, I think I figured my question out. Polynomials of degree b are of the form a0+a1x+a2x^2+...+abx^b in Zn[x]. So you take the number of coefficients, b, and there are only n choices for each coefficient to be (0 to n-1) so the number of...
Does this necessarily mean that there are only 3 homomorphisms in the case of Z6->Z6?
I was under the impression that the number of homomorphisms in this example would be 6! = 720 and only 6 of those would be isomorphisms.
Here was my thought process:
The mappings cycle through, i.e. Z1 maps...
Homework Statement
Show that the number of group homomorphisms from Zn to Zn is equal to n. How many of these are isomorphisms?
The Attempt at a Solution
It has been shown by other proofs that the number of homomorphisms from Zm to Zn is the gcd(m,n), but here m=n, so the gcd(n,n)=n so...
I am wondering how you determine how many polynomials of degree, let's say b, are in Zn[x]. From what I gather, it looks like it does not depend on what b is, but rather what n is. Namely, n^2. Is this correct?