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Zbl 0935.20043
Glasby, S.P.
Subgroups of the upper-triangular matrix groups with maximal derived length and a minimal number of generators. (English)
[A] Campbell, C. M. (ed.) et al., Groups St. Andrews 1997 in Bath. Selected papers of the international conference, Bath, UK, July 26-August 9, 1997. Vol. 1. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 260, 275-281 (1999). ISBN 0-521-65588-9/pbk

Let $U_n$ denote the group of all the $n\times n$ unipotent upper-triangular matrices with entries in a field. In this paper it is shown that $U_n$ has a 3-generated subgroup with derived length $d$, where $2^{d-1}<n\le 2^d$. It is also shown that $U_n$ has a 2-generated subgroup of derived length $d$ if and only if $\tfrac{21}{32}2^d<n\le 2^d$.
[M.R.Darafsheh (Tehran)]

MSC 2000:: *20H20 Other matrix groups over fields
20E07 Subgroup theorems (group theory)
20F14 Series of groups and generalizations
20F05 Presentations of groups

Keywords: unipotent upper-triangular matrices; derived lengths

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