Recent content by Alex Langevub

  1. Alex Langevub

    An exercise with the third isomorphism theorem in group theory

    I assume you meant ##kh_4h_3 \in K/H## and not ##kh_4h_3 \in KH## at the end there.Now, ##\Leftarrow## In an exam I would put a lot more effort into initializeg the different variables ##k_i##, ##g_i## and ##h_i## and justifying each step. If ##K/H \triangleleft G/H##, we have that...
  2. Alex Langevub

    An exercise with the third isomorphism theorem in group theory

    I am still unsure how to go about resolving this problem. I haven't really seen any examples of problems with quotients like this one. So it's the possible manipulations that I am unsure about. Please tell me if this is alright.This problem is an iif so I need to demonstrate both directions ⇐)...
  3. Alex Langevub

    An exercise with the third isomorphism theorem in group theory

    Homework Statement Let ##G## be a group. Let ##H \triangleleft G## and ##K \leq G## such that ##H\subseteq K##. a) Show that ##K\triangleleft G## iff ##K/H \triangleleft G/H## b) Suppose that ##K/H \triangleleft G/H##. Show that ##(G/H)/(K/H) \simeq G/K## Homework Equations The three...
  4. Alex Langevub

    Is the zero Matrix a vector space?

    Homework Statement So I have these two Matrices: M = \begin{pmatrix} a & -a-b \\ 0 & a \\ \end{pmatrix} and N = \begin{pmatrix} c & 0 \\ d & -c \\ \end{pmatrix} Where a,b,c,d ∈ ℝ Find a base for M, N, M +N and M ∩ N. Homework Equations I know the 8 axioms about the vector spaces. The...