table.tex

\section{Table of results}
The variables $x_i$ denote degree one generators, $y_i$ for degree two, etc.
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\begin{center}
  \begin{tabular}{ | c | c | c | c |}
    \hline
    Group & Order & $\rr^*(G)$ & $R^*(G)$ (if unsaturated) \\ [.5em] \hline
    Cyclic $C_N$ & N & $\frac{\ZZ[x]}{(Nx)}$ & sat. \\ [.5em] \hline
    Elementary $C_p^k$ & $p^k$ & $\frac{\ZZ[x_1,\cdots,x_k]}{(px_i, x_i^px_j - x_ix_j^p)}$ & sat.  \\ [.5em] \hline
    Quaternion $Q_8$ & $8$ & $\frac{\ZZ[x_1,x_2,y]}{(2x_i,8y,x_i^2,x_1x_2 - 4y)}$& sat. \\ [.5em] \hline
    Dihedral $D_p$ ($p$ odd) & $2p$ & $\frac{\ZZ[x,y]}{(2x,py,xy)}$ & sat.  \\ [.5em] \hline
    Alternating $A_4$ & $12$ & $\frac{\ZZ[x,y,z]}{(3x,2y,2z, y^2-z^3)}$ & $\frac{\ZZ[x,y]}{(3x,12y,4y + x^2)}$ (partial proof) \\ [.5em] \hline
    Alternating $A_5$ \todo{(wrong!)} & $60$ & $\frac{\ZZ[x_1,x_2,y,z]}{(3x_1,5x_2,2z,2y,y^3-z^3)}$ & probably unsat. \\ [.5em] \hline
    %& & & \\ [.5em] \hline
  \end{tabular}
\end{center}