| Title:
|
On some soluble groups in which $U$-subgroups form a lattice (English) |
| Author:
|
Kurdachenko, Leonid A. |
| Author:
|
Subbotin, Igor Ya. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
585-593 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The article is dedicated to groups in which the set of abnormal and normal subgroups ($U$-subgroups) forms a lattice. A complete description of these groups under the additional restriction that every counternormal subgroup is abnormal is obtained. (English) |
| Keyword:
|
abnormal subgroups |
| Keyword:
|
$U$-subgroups |
| Keyword:
|
counternormal subgroups |
| MSC:
|
20E07 |
| MSC:
|
20E15 |
| MSC:
|
20F16 |
| idZBL:
|
Zbl 1174.20310 |
| idMR:
|
MR2375160 |
| . |
| Date available:
|
2009-05-05T17:04:55Z |
| Last updated:
|
2012-05-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119682 |
| . |
| Reference:
|
[BB] Ba M.S., Borevich Z.I.: On arrangement of intermediate subgroups.in: Rings and Linear Groups, Kubansk. Univ., Krasnodar, 1988, pp.14-41. MR 1206023 |
| Reference:
|
[C] Carter R.W.: Nilpotent self-normalizing subgroups of soluble groups.Math. Z. 75 (1961), 136-139. Zbl 0168.27301, MR 0123603 |
| Reference:
|
[DeFKS] De Falco M., Kurdachenko L.A., Subbotin I.Ya.: Groups with only abnormal and subnormal subgroups.Atti Sem. Mat. Fis. Univ. Modena 46 2 (1998), 435-442. Zbl 0918.20017, MR 1665935 |
| Reference:
|
[F] Fatahi A.: Groups with only normal and abnormal subgroups.J. Algebra 28 (1974), 15-19. MR 0335628 |
| Reference:
|
[KS] Kurdachenko L.A., Subbotin I.Ya.: On transitivity of abnormality.Publ. Math. Debrecen 61 (2002), 3-4 479-486. Zbl 1012.20030, MR 1943708 |
| Reference:
|
[KS1] Kurdachenko L.A., Subbotin I.Ya.: On U-normal subgroups.Southeast Asian Bull. Math. 26 (2003), 789-801. Zbl 1055.20027, MR 2045113 |
| Reference:
|
[KS2] Kurdachenko L.A., Subbotin I.Ya.: Abnormal subgroups and Carter subgroups in some infinite groups.Algebra Discrete Math. 1 (2005), 69-83. Zbl 1092.20027, MR 2148821 |
| Reference:
|
[KNS] Kuzennyi N.F., Subbotin I.Ya: New characterization of locally nilpotent $øverline{IH}$-groups.Ukrain. Mat. Zh. 40 (1988), 322-326 English translation: Ukrainian Math. J. 40 (1988), 274-277. MR 0952119 |
| Reference:
|
[K] Kurosh A.G.: The Theory of Groups.American Mathematical Society, Providence, 1979. Zbl 0111.02502 |
| Reference:
|
[LR] Lennox J.C., Robinson D.J.S.: The Theory of Infinite Soluble Groups.Oxford Mathematical Monographs, Oxford University Press, Oxford, 2004. Zbl 1059.20001, MR 2093872 |
| Reference:
|
[R] Rose J.S.: Nilpotent subgroups of finite soluble groups.Math. Z. 106 (1968), 97-112. Zbl 0169.03402, MR 0252516 |
| Reference:
|
[RD] Robinson D.J.S.: A Course in the Theory of Groups.Springer, New York, 1982. Zbl 0836.20001, MR 0648604 |
| Reference:
|
[S] Subbotin I.Ya.: Groups with alternatively normal subgroups.Izv. Vyssh. Uchebn. Zaved. Mat. 3 (1992), 86-88 English translation: Soviet. Math. 3 (1992), 87-89. Zbl 0816.20030, MR 1204823 |
| . |
