> < ^ Date: Mon, 07 Dec 1992 16:30:04 +0100
> < ^ From: Meinolf Geck <meinolf.geck@math.rwth-aachen.de >
^ Subject: exercises

Hello again!
Recently I sent some latex file containing exercises with GAP. One of them
involved the construction of Janko's smallest group J1. Unfortunately I
mixed up MeatAxe-- and GAP--conventions about finite field elements. So
this exercise needs a further specification:

In order to read into GAP the matrices given in that exercise one has to
proceed as follows:

```a := [ [10,6,6,7,6,7,7], [6,6,7,6,7,7,10], [6,7,6,7,7,10,6], [7,6,7,7,10,6,6],
[6,7,7,10,6,6,7], [7,7,10,6,6,7,6], [7,10,6,6,7,6,7] ]*Z(11);

b := [ [0,6,0,0,0,0,0], [0,0,6,0,0,0,0], [0,0,0,5,0,0,0], [0,0,0,0,6,0,0],
[0,0,0,0,0,5,0], [0,0,0,0,0,0,5], [5,0,0,0,0,0,0] ]*Z(11);
```

So one has to multiply the integer matrices by Z(11), and not by Z(11)^0,
as one might have expected! The vector to be spanned can be calculated as
follows:

```c:=b*a*b*a^2*b*a^3*b^2;
v:=NullspaceMat(c-c^0)[1];
```

The operation of matrices on vectors I have in mind is multiplication of
vectors by matrices: v*a, v*b, etc.

Sorry for this confusion,
Meinolf Geck
Lehrstuhl D f"ur Mathematik
RWTH Aachen

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