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Asked: 2026-05-21T11:29:57+00:00

I have a set of regular (mod 5) matrices N2 and I would like

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I have a set of regular (mod 5) matrices N2 and I would like to get the group generated by these matrices in Mathematica:
My approach was to use a function f doing the matrix multiplication and g for mod 5 and then I wanted to use MapThread

M= Function[{x,y},x.y];
g = Function[z, Mod[z, 5]]
g /@ MapThread[M, {N2,N2}]

The problem is that MapThread is inserting only pairs of elements that are at the same position in the lists. I would like to insert any pair of elements in N. To get the group generated by the matrices in N I would just repeat this and update N2 every time.

E.g. let N2 ={A,B}

g /@ MapThread[M, {N2,N2}]

would return {B^2,A^2}, while I want it to return any product of matrices in N2, i.e. {A^2,AB,BA,B^2}.

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1 Answer

  1. Editorial Team

    In this case you need Outer:

    In[27]:= n = RandomInteger[{1, 5}, {3, 2, 2}];

In[28]:= Outer[mFunc, n, n, 1]

Out[28]= {{mFunc[{{3, 5}, {2, 4}}, {{3, 5}, {2, 4}}], 
  mFunc[{{3, 5}, {2, 4}}, {{3, 4}, {4, 3}}], 
  mFunc[{{3, 5}, {2, 4}}, {{4, 4}, {5, 1}}]}, {mFunc[{{3, 4}, {4, 
     3}}, {{3, 5}, {2, 4}}], 
  mFunc[{{3, 4}, {4, 3}}, {{3, 4}, {4, 3}}], 
  mFunc[{{3, 4}, {4, 3}}, {{4, 4}, {5, 1}}]}, {mFunc[{{4, 4}, {5, 
     1}}, {{3, 5}, {2, 4}}], 
  mFunc[{{4, 4}, {5, 1}}, {{3, 4}, {4, 3}}], 
  mFunc[{{4, 4}, {5, 1}}, {{4, 4}, {5, 1}}]}}

In[29]:= n

Out[29]= {{{3, 5}, {2, 4}}, {{3, 4}, {4, 3}}, {{4, 4}, {5, 1}}}
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