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Math Help - Centre of a Subgroup

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    3

    Centre of a Subgroup

    can someone please help me trying to find the centre of the following subgroup

    H= \begin{pmatrix}<br />
  a & b \\<br />
  0 & c <br />
\end{pmatrix}

    where a,b,c belong to Reals and ac not equal to zero

    ive tried

    \begin{pmatrix}<br />
  a & b \\<br />
  0 & c <br />
\end{pmatrix} <br />
\begin{pmatrix}<br />
  f & g \\<br />
  0 & h <br />
\end{pmatrix}<br />
=<br />
\begin{pmatrix}<br />
  f & g \\<br />
  0 & h <br />
\end{pmatrix}<br />
\begin{pmatrix}<br />
  a & b \\<br />
  0 & c <br />
\end{pmatrix}

    then equating to find the values of a b and c. but have had no luck

    also tried replacing f,g,h with 1's and 0's with no luck

    the answer is Z(H)= \begin{pmatrix}<br />
  a & 0 \\<br />
  0 & a <br />
\end{pmatrix}

    Got an exam in a couple of days so any help appreciated. Can never do these kinds of questions so a general method would be nice.
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  2. #2
    Global Moderator

    Joined
    Nov 2005
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    New York City
    Posts
    10,616
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    10
    Quote Originally Posted by kashk View Post
    can someone please help me trying to find the centre of the following subgroup

    H= \begin{pmatrix}<br />
  a & b \\<br />
  0 & c <br />
\end{pmatrix}

    where a,b,c belong to Reals and ac not equal to zero

    ive tried

    \begin{pmatrix}<br />
  a & b \\<br />
  0 & c <br />
\end{pmatrix} <br />
\begin{pmatrix}<br />
  f & g \\<br />
  0 & h <br />
\end{pmatrix}<br />
=<br />
\begin{pmatrix}<br />
  f & g \\<br />
  0 & h <br />
\end{pmatrix}<br />
\begin{pmatrix}<br />
  a & b \\<br />
  0 & c <br />
\end{pmatrix}

    then equating to find the values of a b and c. but have had no luck

    also tried replacing f,g,h with 1's and 0's with no luck

    the answer is Z(H)= \begin{pmatrix}<br />
  a & 0 \\<br />
  0 & a <br />
\end{pmatrix}

    Got an exam in a couple of days so any help appreciated. Can never do these kinds of questions so a general method would be nice.
    Go here.
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  3. #3
    Newbie
    Joined
    Jan 2009
    Posts
    3
    in the exam we are supposed to do it by reducing the matrix by comparing the coefficients. Is there a way to do this?
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