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The Polycyclic Length of Linear and Finite Polycyclic Groups

Published online by Cambridge University Press:  20 November 2018

R. K. Fisher
R. K. Fisher*
Affiliation:
Carleton University, Ottawa, Ontario
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 4 , August 1974 , pp. 1002 - 1009
Copyright
Copyright © Canadian Mathematical Society 1974

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