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The Polycyclic Length of Linear and Finite Polycyclic Groups
Published online by Cambridge University Press: 20 November 2018
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In what follows, a polycyclic series, for the group G, is any finite series
G = G0 ≧ G1 ≧ . . . ≧ Gl = 1
of subgroups of G, such that Gi+1 ⊲ Gi and Gi/Gi+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.
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- Copyright © Canadian Mathematical Society 1974
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