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- Title
On residual nilpotence of group extensions.
- Authors
Bardakov, V. G.; Bryukhanov, O. V.; Neshchadim, M. V.
- Abstract
We study the following question: under what conditions extension of one residually nilpotent group by another residually nilpotent group is residually nilpotent? We prove some sufficient conditions under which this extension is residually nilpotent. Also, we study this question for semi-direct products and, in particular, for extensions of free group by infinite cyclic group: F n ⋊ φ ℤ. We find conditions under which this group is residually nilpotent, find conditions under which this group has long lower central series. In particular, we prove that for n = 2 the length of the lower central series of F n ⋊ φ ℤ is equal to 2, ω or ω 2 .
- Subjects
GROUP extensions (Mathematics); INFINITE groups; FREE groups; NILPOTENT groups; CYCLIC groups
- Publication
International Journal of Algebra & Computation, 2023, Vol 33, Issue 8, p1617
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196723500613