Geodesic
The Polycyclic Length of Linear and Finite Polycyclic Groups
Canadian journal of mathematics, Tome 26 (1974) no. 4, pp. 1002-1009

Voir la notice de l'article provenant de la source Cambridge University Press

In what follows, a polycyclic series, for the group G, is any finite series G = G 0 ≧ G 1 ≧ . . . ≧ G l = 1of subgroups of G, such that G i+1 ⊲ Gi and Gi /G i+1 is cyclic, for all i = 0, . . ., l — 1. A group that has a polycyclic series is called a polycyclic group, and if G is a polycyclic group, then the polycyclic length of G, which we denote by ρ(G), is the number of non-trivial factors of a polycyclic series for G of shortest length. 
Fisher, R. K. The Polycyclic Length of Linear and Finite Polycyclic Groups. Canadian journal of mathematics, Tome 26 (1974) no. 4, pp. 1002-1009. doi: 10.4153/CJM-1974-093-0
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