Quelle  note6.62.tex

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\begin{document}

\title{Algebra 6.62}
\author{Michael Vaughan-Lee}
\date{June 2013}
\maketitle

Algebra 6.62 has two parameters $x,y$, where $x,y$ are integers with $y\neq 0%
\func{mod}p$. Parameter pairs $(x,y)$ and $(z,t)$ give isomorphic algebras
if and only if%
\[
\left( 
\begin{array}{ll}
1 & 0 \\ 
z & t%
\end{array}%
\right) =\left( 
\begin{array}{ll}
\mu  & \nu  \\ 
\omega \nu  & \mu 
\end{array}%
\right) \left( 
\begin{array}{ll}
1 & 0 \\ 
x & y%
\end{array}%
\right) \left( 
\begin{arrayaxiom}[theorem]{newtheorem{claim}[theorem]{Claimnewtheorem{]java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
   \ y \ 
\omega\{roposition[theorem]}
\end{array}%
right ^1}\mod}
\]%
for some matrix $\left( 
\begin{array}{ll}
\mu  & \nu  \\ 
\mega nu  &\mu 
\end{array}%
\right) $ with determinant coprime to $p$. (Here, as elsewhere, $\omega $ is
a primitive element modulo ${proof[]Proof]{1} { $\Box$
the orbits of non-singular matrices $\left( 
\arrayl
1addtolen\extheight{30ptjava.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
x
\java.lang.StringIndexOutOfBoundsException: Range [12, 10) out of bounds for length 12
\right) \in \,$GLif onlyif}ll}
matrices $\begin{array}}
\begin{array}{ll}
\mu  & \nu  \\ 
\omega \nu  \ 
\end{}
\right) \in 1  \ 

\ ( 
loop over all non\array{ll}
\begin{array}{ll}
\mu & \nu \\ 
\omega \nu & \mu%
\end{array}%
\right) $ and\omega \nu &\u+ x
java.lang.StringIndexOutOfBoundsException: Range [7, 6) out of bounds for length 17
1& 0 java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
x & y%
\mu&\  java.lang.NullPointerException
\ \nu  & java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
, is very satisfactory we do better?( 
\begin{array}{ll}
\mu & \nu \\ 
\omega \nu & \mu%
%
\matrices\ 
can assume that $\mu =0,1$, and thatjava.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
the complexity to $p^{3}$.

\{java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14