Discrete mathematics

Organic chemistry

Pure mathematics

Mathematics

Finite field

Chemistry

Unipotent

Group (periodic table)

Conjugacy class

Field (mathematics)

Journal of Group Theory

We prove a formula connecting the number of unipotent conjugacy classes in a maximal parabolic subgroup of a finite general linear group with the numbers of unipotent conjugacy classes in various parabolic subgroups in smaller dimensions. We generalize this formula and deduce a number of corollaries; in particular, we express the number of conjugacy classes of unitriangular matrices over a finite field in terms of the numbers of unipotent conjugacy classes in maximal parabolic subgroups over the same field. We show how the numbers of unipotent conjugacy classes in parabolic subgroups of small dimensions may be calculated.

Conjugacy classes in parabolic subgroups of general linear groups