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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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