Skip to main content
1 of 4
Chunna
  • 529
  • 2
  • 9

Conjugacy classes of GL(3,ZZ)

We know that every $2\times 2$ matrix of order 3 is conjugate to the matrix [ \left (\begin{array}{cc} 1 & -1 \\ 1 & 0 \end{array} \right) ]. I am interested in finding out to what extent this holds for $3\times 3$ integer invertible matrices.

In other words how many conjugacy classes of order 3 matrices in $GL(3, \mathbb Z)$ are there?

Chunna
  • 529
  • 2
  • 9