Lower central depth in finitely generated soluble-by-finite groups
Glasgow mathematical journal, Tome 19 (1978) no. 2, pp. 153-154
Voir la notice de l'article provenant de la source Cambridge University Press
We say that a group G has finite lower central depth (or simply, finite depth) if the lower central series of G stabilises after a finite number of steps.In [1], we proved that if G is a finitely generated soluble group in which each two generator subgroup has finite depth then G is a finite-by-nilpotent group. Here, in answer to a question of R. Baer, we prove the following stronger version of this result.
Lennox, John C. Lower central depth in finitely generated soluble-by-finite groups. Glasgow mathematical journal, Tome 19 (1978) no. 2, pp. 153-154. doi: 10.1017/S0017089500003554
@article{10_1017_S0017089500003554,
author = {Lennox, John C.},
title = {Lower central depth in finitely generated soluble-by-finite groups},
journal = {Glasgow mathematical journal},
pages = {153--154},
year = {1978},
volume = {19},
number = {2},
doi = {10.1017/S0017089500003554},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500003554/}
}
TY - JOUR AU - Lennox, John C. TI - Lower central depth in finitely generated soluble-by-finite groups JO - Glasgow mathematical journal PY - 1978 SP - 153 EP - 154 VL - 19 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500003554/ DO - 10.1017/S0017089500003554 ID - 10_1017_S0017089500003554 ER -
[1] 1.Lennox, J. C., Finitely generated soluble groups in which all subgroups have finite lower central depth, Bull. London Math. Soc. 7 (1975), 273–278. Google Scholar
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[3] 3.Robinson, D. J. S., Finiteness conditions and generalised soluble groups, Vol II (Springer, 1972). Google Scholar
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