The Fibonacci length of certain centro-polyhedral groups
β 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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π SIMILAR VOLUMES
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.
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