The Unipotency of Eleventh Order Matrix Group with no More than Seven Jordan Blocks

Abstract

By avoiding complex research methods involving Lie algebra and Lie superalgebra, and instead utilizing simple theories such as matrix logarithm and expansion of product of non commutative polynomial, the new combination property of primitive elements of binary generated free groups is explored intensively against the problem of unipotent of binary generated matrix groups. A unified proof of the combination property is given for the general matrix group initiatively using the primitive elements of the binary generated free group with a new equation for the matrix trace obtained. Based on this, a flowchart is primarily used to summarize the proofing process. At the same time, the equation is solved by maple, the calculation software, before the new judgment condition of the unipotency is obtained from the similarity transformation. This approach enriches the content of related research.

Keywords

• primitive element
• matrix group
• unipotency
• free group