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The Fibonacci length of certain centro-polyhedral groups

✍ Scribed by C. M. Campbell; P. P. Campbell


Publisher
Springer-Verlag
Year
2005
Tongue
English
Weight
208 KB
Volume
19
Category
Article
ISSN
1598-5865

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In this note we prove two results concerned with the derived length of p-groups. First, we improve a little a lower bound of P. Hall for the order of a group of a given derived length. Next, we improve a bound for the derived length of a product of two p-groups.

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Let G be a polycyclic group. We prove that if the nilpotent length of each finite quotient of G is bounded by a fixed integer n, then the nilpotent length of G is at most n. The case n s 1 is a well-known result of Hirsch. As a consequence, we obtain that if the nilpotent length of each 2-generator