Recent content by burritoloco

Hi, I'm new to this subject and wondering if anything is known specifically on the zero-th Gaussian periods of type (N,r), where N is a product of distinct primes and r = p^s is a power of a prime. I know there are some very general results out there, but I haven't seen this so far. Thanks...

Homework Statement Hi, suppose we have the summation \sum_{i=0}^{n-1} \sum_{j=0}^{n-1} a_j b_{i-j}^{j} x^i, where the subscripts are taken modulo n, and a_i^n = a_i, b_i^n = b_i for each i. Write the above power series as a product of two power series modulo x^n - x.Homework Equations I'm...

For instance, the example that I gave for g has the image of id - f contained in its kernel, but I'm not sure that we can show the converse is true in all cases of f .

Thank you. Now, suppose that we restrict g so that its kernel is the image of id - f . One can show that this g also satisfies g = g \circ f^i for each i \geq 0 . Any ideas whether it would be possible to obtain an expression for g in terms of f or so?

If not a general formula, it would be nice to have as many examples as possible, like the above. OK, I understand what you mean now (after a good night sleep! hehe). Thanks. But as you can see from the previous post I'm more interested in, given f, what are the g's satisfying this? It might be...

Thanks lurflurf. I'm not sure I understand why it defines a partition. But I was particularly interested in knowing whether there is a general formula for the linear maps g satisfying g = g \circ f^i, in terms of f. For instance, the fact that we have a finite field guarantees that we can find...

Remark: In the 2nd question, f doesn't have to satisfy the property in the 1st question.

Hi, Let f be a linear transformation over some finite field, and denote f^{n} := f \circ f \circ \cdots \circ f, n times. What do we know about the linear maps f such that there exist an integer n for which f^{N} = f^n for all N \geq n? Also, how about linear maps g satisfying g = g \circ f^i...

Perfect, thank you. The vectors that are not in the span of the subspace basis are just sent to 0!

Intuitively I think it makes sense a surjection exists.

"Another related question: If I have a group isomorphism between two normal subgroups of two equally sized finite groups, then would the two groups also be isomorphic? And if so, would the same mapping of the normal subgroups (showing their isomorphism) also imply the group isomorphism?" I just...

Rightly guessed!

Ahh, now I see that I should have mentioned that I'm actually dealing with vector spaces instead of groups lol. D_6 is not abelian..

Thank you for that :)

I forgot to mention that for the first question the image is also contained within the group, if this is of any use. Also, I'm wondering whether we could even guarantee a surjection from a group to any of its normal subgroups?