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  1. M

    Algebraic expressions - simplifying

    It shouldn't be too terrible. The obvious thing to note is that (b - a) = -(a - b), for example.
  2. M

    Cyclic Subgroup of GL(2,q)

    It seems like you're going about the problem correctly except that obviously the splitting field won't be as described if the quadratic is reducible. Other than that, unless I'm forgetting something (which would hardly be surprising), what you're saying is completely true.
  3. M

    Generation of isomorphic fields by separate algebraic elements

    Ah, of course. I must have been thinking of something else. I've gotta stop posting when I haven't slept.
  4. M

    Generation of isomorphic fields by separate algebraic elements

    Er...aren't those fields are isomorphic? Take a map that's identity on the rationals, and root 2 mapped to root 3, right? I mean, strictly speaking I don't think that the degree being the same is enough to guarantee an isomorphism (if I had to guess, I'd say the automorphism groups of the...
  5. M

    Identity map and injectivity

    By the way, my example map is completely wrong. That's what happens when you answer algebra questions while doing complex analysis I suppose.
  6. M

    Identity map and injectivity

    I don't think this is true unless you assume U and V have the same dimension. For T to be injective, it must be the case that dim V \geq dim U, but equality doesn't have to hold. However, there does have to be an S such that ST is the identity on U (namely you just take Sx to be the preimage...
  7. M

    Identity map and injectivity

    What's the definition of injectivity? How could you use that to define a function from W to V?
  8. M

    Matrix Binomials ?

    Okay, so I'm sure you noticed that M = aX + bY. Then M^n = (aX + bY)^n, right? Now, if X and Y were just plain old real numbers (or variables if you like), what would you do to expand (aX + bY)^n
  9. M

    Who takes Linear Algebra?

    All of the above. If not in a specific linear algebra/matrix algebra course, then as part of some other course.
  10. M

    Coset representation?

    I believe a coset representative would be the a in aH. Of course, talking about "coset representatives" when H isn't a normal subgroup is a little odd. For one, if H isn't a subgroup, the "representative" might be unique, and that's bad for most things you want to do with cosets (like in your...
  11. M

    Classification of groups

    Yeah, I think groups of order pq work. Also, I think a cyclic group of order p^3 works...
  12. M

    Classification of groups

    I was wondering about the classification of groups with a certain number of subgroups. I (sort of mostly I think maybe) get the ideas behind classification of groups of a certain (hopefully small) order, but I came across a question about classifying all groups with exactly 4 subgroups, and I...