> < ^ Date: Mon, 14 Aug 2000 12:20:17 -0400
> < ^ From: David Joyner <wdj@usna.edu >
> ^ Subject: matrix groups over a ring
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Dear GAP Forum:
Does anyone know an easy way to construct a matrix group over a
ring such as Z/p^nZ in GAP? For example, I've tried constructing the
ring R of 2x2 matrices
over Z/9Z, for example, using something like
R:=MatrixAlgebra(ZmodnZ(9),2),
but then Units(R) returns the empty list. (I expected "Units(R);" to
return the group
GL(2,Z/9Z).) The same thing happens when I use
Full MatrixModule(ZmodnZ(9),2,2),
for example.
Eventually, I'd like to convert such a group into a permutation group
and
study it's representations. - David Joyner

--
David Joyner, wdj@usna.edu, Prof Math Dept, USNA, Annapolis, MD, USA
office: 410-293-6738, Chauvenet Hall 328, URL: http://tinah.mslab.usna.edu/

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<html>
&nbsp;&nbsp; Dear GAP&nbsp;Forum:
<br>&nbsp; Does anyone know an easy way to construct a matrix group over
a
<br>ring such as Z/p^nZ in GAP? For example, I've tried constructing the
ring R of 2x2 matrices
<br>over Z/9Z, for example, using something like
<br>R:=MatrixAlgebra(ZmodnZ(9),2),
<br>but then Units(R) returns the empty list. (I expected "Units(R);" to
return the group
<br>GL(2,Z/9Z).) The same thing happens when I use
<br>Full MatrixModule(ZmodnZ(9),2,2),
<br>for example.
<br>&nbsp;Eventually, I'd like to convert such a group into a permutation
group and
<br>study it's representations. - David Joyner
<pre>--&nbsp;
David Joyner, wdj@usna.edu, Prof Math Dept, USNA, Annapolis, MD, USA
office: 410-293-6738, Chauvenet Hall 328, URL: <A HREF="http://tinah.mslab.usna.edu/">http://tinah.mslab.usna.edu/</A></pre>
&nbsp;</html>

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