Geodesic
Covering a group with isolators of finitely many subgroups
Glasgow mathematical journal, Tome 35 (1993) no. 2, pp. 253-259

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

In [6] B. H. Neumann proved the following beautiful result: if a group G is covered by finitely many cosets, say G = xiHi, then we can omit from the union any xiHi, for which |G|Hj| is infinite. In particular, |G:Hj| is finite, for some j ∈ {l,...,n}.In an unpublished result R. Baer characterized the groups covered by finitely many abelian subgroups, they are exactly the centre-by-finite groups [8]. Coverings by nilpotent subgroups or by Engel subgroups and by normal subgroups have been studied, for example, by R. Baer (see [8]), L. C. Kappe [2,1], M. A. Brodie and R. F. Chamberlain [1], and recently by M. J. Tomkinson [9]. 
Longobardi, Patrizia; Maj, Mercede; Rhemtulla, Akbar H. Covering a group with isolators of finitely many subgroups. Glasgow mathematical journal, Tome 35 (1993) no. 2, pp. 253-259. doi: 10.1017/S0017089500009812
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[1] 1.Brodie, M. A., Chamberlain, R. F. and Kappe, L.-C., Finite coverings by normal subgroups, Proc. Amer. Math. Soc., 104 no. 3 (1988), 669–674. Google Scholar | DOI

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

[3] 3.Kirkinskii, A. S., Intersection of finitely generated subgroups in metabelian groups, Algebra and Logic, 20 no. 1 (1981), 22–36 (Algebra i Logika, 37–54). Google Scholar | DOI

[4] 4.Lennox, J. C., Bigenetic properties of finitely generated hyper-(abelian-by-finite) groups, J. Austral. Math. Soc., 16 (1973), 309–315. Google Scholar | DOI

[5] 5.Lennox, J. C. and Wiegold, J., Extension of a problem of Paul Erdös on groups, J. Austral. Math. Soc., Ser. A, 31 (1981), 459–463. Google Scholar | DOI

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

[7] 7.Rhemtulla, A. H. and Wehrfritz, B. A. F., Isolators in soluble groups of finite rank, Rocky Mountain J. Math., 14 no. 2 (1984), 415–421. Google Scholar | DOI

[8] 8.Robinson, D. J. S., Finiteness conditions and generalized soluble groups, vol. I, II, Springer-Verlag, Berlin–New York, 1972. Google Scholar | DOI

[9] 9.Tomkinson, M. J., Hypercentre-by-finite groups, Publ. Math. Debrecen 40 (1992), 313–321. Google Scholar | DOI

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