Subgroups of the upper-triangular matrix group with maximal derived length and a minimal number of generators
Group Theory
2014-10-21 v1
Abstract
The group U_n(F) of all nxn unipotent upper-triangular matrices over F has derived length d := Ceiling(log_2 (n)), equivalently 2^{d-1} < n <= 2^d. We prove that U_n(F) has a 3-generated subgroup of derived length d, and it has a 2-generated subgroup of derived length d if and only if (21/32)* 2^d < n <= 2^d.
Keywords
Cite
@article{arxiv.1410.5052,
title = {Subgroups of the upper-triangular matrix group with maximal derived length and a minimal number of generators},
author = {S. P. Glasby},
journal= {arXiv preprint arXiv:1410.5052},
year = {2014}
}
Comments
Differs from original publication because: an abstract is added, statement of main theorem is simplified, and retyped in LaTeX2e with hyperlinks. 9 pages