Geodesic
Finite coverings by subgroups with a given property
Glasgow mathematical journal, Tome 35 (1993) no. 2, pp. 179-188

Voir la notice de l'article provenant de la source Cambridge University Press

Let be a group-theoretic property. We say a group has a finite covering by -subgroups if it is the set-theoretic union of finitely many -subgroups. The topic of this paper is the investigation of groups having a finite covering by nilpotent subgroups, n-abelian subgroups or 2-central subgroups.R. Baer [12; 4.16] characterized central-by-finite groups as those groups having a finite covering by abelian subgroups. In [6] it was shown that [G: ZC (G)] finite implies the existence of a finite covering by subgroups of nilpotency class c, i.e. Rc-groups. However, an example of a group is given there which has a finite covering by R2-groups, but Z2(G) does not have finite index in the group. These results raise two questions, on which we will focus our investigations. 
Brodie, Marc A.; Kappe, Luise-Charlotte. Finite coverings by subgroups with a given property. Glasgow mathematical journal, Tome 35 (1993) no. 2, pp. 179-188. doi: 10.1017/S0017089500009733
@article{10_1017_S0017089500009733,
     author = {Brodie, Marc A. and Kappe, Luise-Charlotte},
     title = {Finite coverings by subgroups with a given property},
     journal = {Glasgow mathematical journal},
     pages = {179--188},
     year = {1993},
     volume = {35},
     number = {2},
     doi = {10.1017/S0017089500009733},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009733/}
}
TY  - JOUR
AU  - Brodie, Marc A.
AU  - Kappe, Luise-Charlotte
TI  - Finite coverings by subgroups with a given property
JO  - Glasgow mathematical journal
PY  - 1993
SP  - 179
EP  - 188
VL  - 35
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009733/
DO  - 10.1017/S0017089500009733
ID  - 10_1017_S0017089500009733
ER  - 
%0 Journal Article
%A Brodie, Marc A.
%A Kappe, Luise-Charlotte
%T Finite coverings by subgroups with a given property
%J Glasgow mathematical journal
%D 1993
%P 179-188
%V 35
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009733/
%R 10.1017/S0017089500009733
%F 10_1017_S0017089500009733

[1] 1.Baer, R., Endlichkeitskriterien für Kommutatorgruppen, Math. Annalen 124 (1952), 166–177. Google Scholar

[2] 2.Baer, R., Factorization of n-soluble and n-nilpotent groups, Proc. Amer. Math. Soc. 4 (1953), 15–26. Google Scholar

[3] 3.Brodie, M. A., Chamberlain, R. F. and Kappe, L. C., Finite coverings by normal subgroups, Proc. Amer. Math. Soc. 104 (1988), 669–674. Google Scholar | DOI

[4] 4.Dietrich, A., Durch Einbettung beschriebene charakteristische Untergruppen, Diplomarbeit, Würzburg, 1990. Google Scholar

[5] 5.Hall, P., Verbal and Marginal Subgroups, J. Reine Angew. Math. 182 (1940), 156–157. Google Scholar | DOI

[6] 6.Kappe, L. C., Finite coverings by 2-Engel groups, Bull. Austral. Math. Soc. 38 (1988), 141–150. Google Scholar | DOI

[7] 7.Kappe, L. C. and Morse, R. F., Groups with 3-abelian normal closures, Arch. Math. 51 (1988), 104–110. Google Scholar | DOI

[8] 8.Kappe, L. C. and Newell, M. L., On the n-centre of a group, Groups St. Andrews 1989, LMS Lecture Notes 160 (1991), 339–352. Google Scholar | DOI

[9] 9.Neumann, B. H., Groups covered by finitely many cosets, Publ. Math. Debrecen 3 (1954), 227–242. Google Scholar | DOI

[10] 10.Neumann, B. H., Groups covered by permutable subsets, J. London Math. Soc. 29 (1954), 236–248. Google Scholar | DOI

[11] 11.Neumann, B. H., A problem of Paul Erdös on groups, J. Austral. Math. Soc. 21 A (1976), 467–472. Google Scholar | DOI

[12] 12.Robinson, D. J. S., Finiteness conditions and generalized soluble groups, Part I, (Springer-Verlag 1972). Google Scholar | DOI

Cité par Sources :