| Title:
|
Groups with the weak minimal condition for non-subnormal subgroups II (English) |
| Author:
|
Kurdachenko, Leonid A. |
| Author:
|
Smith, Howard |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
601-605 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 {\it 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. (English) |
| Keyword:
|
subnormal subgroups |
| Keyword:
|
soluble-by-finite groups |
| MSC:
|
20E15 |
| MSC:
|
20F19 |
| MSC:
|
20F22 |
| idZBL:
|
Zbl 1106.20023 |
| idMR:
|
MR2259493 |
| . |
| Date available:
|
2009-05-05T16:53:45Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119553 |
| . |
| Reference:
|
[DES] Dixon M.R., Evans M.J., Smith H.: Locally (soluble-by-finite) groups of finite rank.J. Algebra 182 (1996), 756-769. Zbl 0854.20037, MR 1398121 |
| Reference:
|
[KS1] Kurdachenko L.A., Smith H.: Groups with the weak minimal condition for non-subnormal subgroups.Ann. Mat. Pura Appl. 173 (1997), 299-312. Zbl 0939.20040, MR 1625608 |
| Reference:
|
[KS2] Kurdachenko L.A., Smith H.: Groups with the weak maximal condition for non-subnormal subgroups.Ricerche Mat. 47 (1998), 29-49. Zbl 0928.20025, MR 1760322 |
| Reference:
|
[Me] Merzlyakov Yu.I.: Locally soluble groups of finite rank.Algebra i Logika 3 (1964), 5-16; Erratum 8 (1969), 686-690. MR 0289647 |
| Reference:
|
[Mö] Möhres W.: Auflösbarkeit von Gruppen, deren Untergruppen alle subnormal sind.Arch. Math. (Basel) 54 (1990), 232-235. MR 1037610 |
| Reference:
|
[R] Robinson D.J.S.: Finiteness conditions and generalized soluble groups.2 vols., Springer, Berlin, 1972. Zbl 0243.20033 |
| Reference:
|
[Z] Zai'cev D.I.: Theory of minimax groups.Ukrainian Math. J. 23 (1971), 536-542. MR 0294512 |
| . |
