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Zbl 1115.20012
Glasby, S.P.
The shape of solvable groups with odd order. (English)
[A] Campbell, C.M. (ed.) et al., Groups St. Andrews 2005. Vol. II. Selected papers of the conference, St. Andrews, UK, July 30--August 6, 2005. Cambridge: Cambridge University Press. London Mathematical Society Lecture Note Series 340, 432-437 (2007). ISBN 978-0-521-69470-4/pbk

Summary: The minimal composition length, $c$, of a solvable group with solvable length $d$ satisfies $9^{(d-3)/9}< c<9^{(d+1)/5}$. The minimal composition length, $c^o$, of a group with odd order and solvable length $d$ satisfies $7^{(d-2)/5}<c^o<2^d$.

MSC 2000:: *20D10 Solvable finite groups
20D30 Series and lattices of subgroups of finite groups
20D60 Arithmetic and combinatorial problems on finite groups

Keywords: finite solvable groups; composition lengths; solvable lengths; derived lengths

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