Groups with the weak minimal condition for non-subnormal subgroups II
Leonid A. Kurdachenko; Howard Smith
Commentationes Mathematicae Universitatis Carolinae (2005)
- Volume: 46, Issue: 4, page 601-605
- ISSN: 0010-2628
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topKurdachenko, Leonid A., and Smith, Howard. "Groups with the weak minimal condition for non-subnormal subgroups II." Commentationes Mathematicae Universitatis Carolinae 46.4 (2005): 601-605. <http://eudml.org/doc/249535>.
@article{Kurdachenko2005,
abstract = {Let $G$ be a group with the property that there are no infinite descending chains of non-subnormal subgroups of $G$ for which all successive indices are infinite. The main result is that if $G$ is a locally (soluble-by-finite) group with this property then either $G$ has all subgroups subnormal or $G$ is a soluble-by-finite minimax group. This result fills a gap left in an earlier paper by the same authors on groups with the stated property.},
author = {Kurdachenko, Leonid A., Smith, Howard},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {subnormal subgroups; soluble-by-finite groups; subnormal subgroups; soluble-by-finite groups},
language = {eng},
number = {4},
pages = {601-605},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Groups with the weak minimal condition for non-subnormal subgroups II},
url = {http://eudml.org/doc/249535},
volume = {46},
year = {2005},
}
TY - JOUR
AU - Kurdachenko, Leonid A.
AU - Smith, Howard
TI - Groups with the weak minimal condition for non-subnormal subgroups II
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 4
SP - 601
EP - 605
AB - Let $G$ be a group with the property that there are no infinite descending chains of non-subnormal subgroups of $G$ for which all successive indices are infinite. The main result is that if $G$ is a locally (soluble-by-finite) group with this property then either $G$ has all subgroups subnormal or $G$ is a soluble-by-finite minimax group. This result fills a gap left in an earlier paper by the same authors on groups with the stated property.
LA - eng
KW - subnormal subgroups; soluble-by-finite groups; subnormal subgroups; soluble-by-finite groups
UR - http://eudml.org/doc/249535
ER -
References
top- Dixon M.R., Evans M.J., Smith H., Locally (soluble-by-finite) groups of finite rank, J. Algebra 182 (1996), 756-769. (1996) Zbl0854.20037MR1398121
- Kurdachenko L.A., Smith H., Groups with the weak minimal condition for non-subnormal subgroups, Ann. Mat. Pura Appl. 173 (1997), 299-312. (1997) Zbl0939.20040MR1625608
- Kurdachenko L.A., Smith H., Groups with the weak maximal condition for non-subnormal subgroups, Ricerche Mat. 47 (1998), 29-49. (1998) Zbl0928.20025MR1760322
- Merzlyakov Yu.I., Locally soluble groups of finite rank, Algebra i Logika 3 (1964), 5-16; Erratum 8 (1969), 686-690. (1964) MR0289647
- Möhres W., Auflösbarkeit von Gruppen, deren Untergruppen alle subnormal sind, Arch. Math. (Basel) 54 (1990), 232-235. (1990) MR1037610
- Robinson D.J.S., Finiteness conditions and generalized soluble groups, 2 vols., Springer, Berlin, 1972. Zbl0243.20033
- Zai'cev D.I., Theory of minimax groups, Ukrainian Math. J. 23 (1971), 536-542. (1971) MR0294512
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