On conjugacy classes of GL(n,q) and SL(n,q)

Adan-Bante, Edith; Harris, John M.

On conjugacy classes of GL(n,q) and SL(n,q)

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Let GL(n,q) be the group of nxn invertible matrices over a field with q elements, and SL(n,q) be the group of nxn matrices with determinant 1 over a field with q elements. We prove that the product of any two non-central conjugacy classes in GL(n,q) is the union of at least q-1 distinct conjugacy classes, and that the product of any two non-central conjugacy classes in SL(n,q) is the union of at least $\lceil\frac{q}{2} \rceil$ distinct conjugacy classes.
9 pages