Recent content by zoek

  1. Z

    Graduate Left group actions involving SO(3) and the 2-sphere

    for the second part You have a transitive action of G=SO(3) on the set A=S^2 and G_r the isotropy group of r. You know that G acts on G/G_r - by g\cdot xG_r = gxG_r. You have to define a bijection f: G/G_r \to A such that "G has identical action on A and on G/G_r". I think that this...
  2. Z

    Graduate Showing that a map from factor group to another set bijective

    g_1 H = g_2 H \implies g_2^{-1}g_1 H = H \implies g_2^{-1}g_1 \in H \implies g_2^{-1}g_1 \cdot x=x \implies g_1 \cdot x = g_2 \cdot x \implies f(g_1 H) = f(g_2 H). This is OK. You need to start with an arbitrary y in X. Since G is transitive there exist g\in G such that g \cdot x = y...
  3. Z

    Lets say you have a set S = {1, 2, 3}

    yes - the set {1, 2} is equal to {2, 1}.
  4. Z

    Graduate When p(A)=0 iff p(B)=0 for any polynomial,why same minimal polynomial?

    Let m_A, m_B be the minimal polynimials of A and B. Then m_A (A) = 0\Rightarrow m_A (B) = 0 \Rightarrow m_B / m_A^{(1)} and m_B (B) = 0\Rightarrow m_B (B) = 0 \Rightarrow m_A / m_B ^{(2)} \overset {(1), (2)}{\Rightarrow} m_A = k \cdot m_B with k a constant. But m_A, m_B are both monic...