> < ^ Date: Wed, 31 Oct 2001 10:46:29 -0500
< ^ From: George McNinch <mcninch.1@nd.edu >
< ^ Subject: Re: bug ?

>>>"Hulpke" == Alexander Hulpke <hulpke@math.colostate.edu> writes:

Hulpke> However (as also noted) now GAP 4.2 will stop with an
Hulpke> error message (``No method found'') that indicates that
Hulpke> the capability to test invertibility of a matrix in this
Hulpke> ring has not been implemented.

Except that GAP does seem to be able to decide invertibility:

```gap> R := Integers mod 9;
(Integers mod 9)
gap> S := FullMatrixAlgebra(R,2);
( (Integers mod 9)^[ 2, 2 ] )
gap> one := Identity(R); zero := Zero(R);
ZmodnZObj( 1, 9 )
ZmodnZObj( 0, 9 )
gap> x := [[one,one],[zero,one]];
[ [ ZmodnZObj( 1, 9 ), ZmodnZObj( 1, 9 ) ],
[ ZmodnZObj( 0, 9 ), ZmodnZObj( 1, 9 ) ] ]
gap> IsUnit(S,x);
true
```

And one can even generate SL(2,Z/9Z):

```gap>  y := [[one,zero],[one,one]];
[ [ ZmodnZObj( 1, 9 ), ZmodnZObj( 0, 9 ) ],
[ ZmodnZObj( 1, 9 ), ZmodnZObj( 1, 9 ) ] ]
gap> Order(Group(x,y));
648
gap> 3*4*2*27;
648
```

It seems like the group just mentioned must be constructed
as a subgroup of Units(S). (??)

[Sorry if I'm creating too much noise on this list...]

All the best,
George

```--
__O        |  George McNinch <mcninch.1@nd.edu>
_-\<,_       |  www.nd.edu/~gmcninch
(_)/ (_)      |  Dept. Math, Univ. Notre Dame
```

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