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Action of Reflection Groups on Nilpotent Groups

✍ Scribed by F. Zara

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
339 KB
Volume
18
Category
Article
ISSN
0195-6698

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πŸ“œ SIMILAR VOLUMES

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Let C C be a class of groups, closed under taking subgroups and quotients. We prove that if all metabelian groups of C C are torsion-by-nilpotent, then all soluble groups of C C are torsion-by-nilpotent. From that, we deduce the following conse-Ε½ quence, similar to a well-known result of P. Hall 195

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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

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