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arXiv · 1410.5052

Subgroups of the upper-triangular matrix group with maximal derived length and a minimal number of generators

S. P. Glasby
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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.

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S. P. Glasby. 2014-10-19. Subgroups of the upper-triangular matrix group with maximal derived length and a minimal number of generators. https://arxiv.org/abs/1410.5052

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