The Unipotency of Linear Groups Generated by Matrices with No More than Five Jorden Blocks - YANG Xin-song; LI Jia-xin (Journal of Harbin University of Science and Technology)
Aiming at the question whether the group generated by two unipotent matrices whose Jordan blocks are of order no more than five is a unipotent group, based on the fundamental definition of nilpotent matrix, we use the matrix logarithm tool to obtain some combinatorial properties of the generators of free groups, and then use the combinatorial properties obtained to carry out theoretical derivation, and finally prove that the group generated by the matrices whose block are of order no more than five is a unipotent group if every primitive is unipotent and their Jordan blocks are of order no more than five. We also strive to provide new ideas and methods for studying the related properties of unipotency.