I have the following Beamer document, but I get errors in the frame shown. Any ideas what the problem might be and how to solve it?



  \usetheme{default}      % or try Darmstadt, Madrid, Warsaw, ...
  \usecolortheme{default} % or try albatross, beaver, crane, ...
  \usefonttheme{default}  % or try serif, structurebold, ...
  \setbeamertemplate{navigation symbols}{}



\graphicspath{ {images/} }




\begin{frame}{Group structure}
  \begin{block}{Torsion structure}
    Let $E$ be defined over an algebraically closed field $\bar{k}$ of
    characteristic $p$.
      E[m] \simeq\quad& \ZZ/m\ZZ\times\ZZ/m\ZZ  &\text{if p\nmid m,}\\[1em]
                 &\ZZ/p^e\ZZ & \text{\emph{ordinary} case,}\\[-1.7em]
      E[p^e] \simeq\Biggl\{& \\[-1.7em]
                 &\{\O\} & \text{\emph{supersingular} case.}


The first error is that \text puts its content in text mode so you need $ to get back to math

 \text{if $p\nmid m$,}

The second error is that cases is a two-column alignment so you can only have one & you could use

             \{\O\} & \text{\emph{supersingular} case.}

which has one & so error free but a cases alignment with only one row doesn't serve any purpose, so I am not sure of the intended layout there.


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