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Zbl 1082.20007
Glasby, S.P.
Solvable groups with a given solvable length, and minimal composition length. (English)
[J] J. Group Theory 8, No. 3, 339-350 (2005). ISSN 1433-5883; ISSN 1435-4446

The author denotes by $c_S(d)$ the minimal composition length of all finite solvable groups with derived length $d$ and $c_N(d)$ the minimal composition length of the finite nilpotent groups with derived length $d$. It is shown that $c_S(d)$ grows exponentially and that for large $d$ $c_S(d)$ is considerably smaller than $c_N(d)$.\par The main result of the paper establishes the exact values for $c_S(d)$ for $d\leq 8$; for example, $c_S(8)=15$. -- The proof is complicated and consists of a careful case by case analysis of the various possible configurations.
[Marian Deaconescu (Safat)]

MSC 2000:: *20D10 Solvable finite groups
20D15 Nilpotent finite groups
20D30 Series and lattices of subgroups of finite groups
20D60 Arithmetic and combinatorial problems on finite groups

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

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