Recent content by Menelaus

  1. M

    Prove that, if f(x) is differentiable at x =c , then f(x) is continous at x=c

    Use the definition of limit to make an inequality (< ε for some ε > 0) to get yourself started and simplify. From there it is useful to change your x's into x_{n}'s
  2. M

    Graduate Why is G abelian if |G/Z(G)|=p with p prime?

    I do not follow, I don't believe I've ever looked at this sequence or talked about what a split sequence is. Micromass cleared up the problem I was having though.
  3. M

    Graduate Why is G abelian if |G/Z(G)|=p with p prime?

    Ah I see! Thanks for clearing that up.
  4. M

    Graduate Why is G abelian if |G/Z(G)|=p with p prime?

    I am aware of the theorem |G/Z(G)|=p with p prime implies G/Z(G) is cyclic and thus G is abelian, but I do not understand why. Is there not a theorem that says G abelian \Leftrightarrow Z(G)=G? So what if |G|=p^{3} and |Z(G)|=p^{2}? This implies |G/Z(G)|=p implying G is abelian however...
  5. M

    What is the Normalizer of a Subgroup?

    Should I post this in the Linear Algebra thread? The rules say not to but it seems to me that questions such as this get answered there. I'm really just looking for if my solution is valid or not as well as a hint for the infinite case..
  6. M

    What is the Normalizer of a Subgroup?

    Homework Statement Prove the number of distinct conjugate subgroups of a subgroup H in a group G is [G:N(H)] where N(H)={g \in G | gHg^{-1}=H}. Homework Equations I'm thinking the counting formula; G=|C(x)||Z(x)| with C(x) being the conjugacy class of x and Z(x) being the centralizer...