In this paper we investigate the structure of X-groups in which every subgroup is permutable or of finite rank. We show that every subgroup of such a group is permutable.
@article{bwmeta1.element.doi-10_2478_s11533-012-0012-z, author = {Martyn Dixon and Yalcin Karatas}, title = {Groups with all subgroups permutable or of finite rank}, journal = {Open Mathematics}, volume = {10}, year = {2012}, pages = {950-957}, zbl = {1258.20022}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0012-z} }
Martyn Dixon; Yalcin Karatas. Groups with all subgroups permutable or of finite rank. Open Mathematics, Tome 10 (2012) pp. 950-957. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0012-z/
[1] Baer R., Heineken H., Radical groups of finite abelian subgroup rank, Illinois J. Math., 1972, 16(4), 533–580 | Zbl 0248.20052
[2] Chernikov N.S., A theorem on groups of finite special rank, Ukrainian Math. J., 1990, 42(7), 855–861 http://dx.doi.org/10.1007/BF01062091
[3] De Falco M., De Giovanni F., Musella C., Schmidt R., Groups in which every non-abelian subgroup is permutable, Rend. Circ. Mat. Palermo, 2003, 52(1), 70–76 http://dx.doi.org/10.1007/BF02871925 | Zbl 1072.20038
[4] Dixon M.R., Evans M.J., Smith H., Locally (soluble-by-finite) groups of finite rank, J. Algebra, 1996, 182(3), 756–769 http://dx.doi.org/10.1006/jabr.1996.0200
[5] Evans M.J., Kim Y., On groups in which every subgroup of infinite rank is subnormal of bounded defect, Comm. Algebra, 2004, 32(7), 2547–2557 http://dx.doi.org/10.1081/AGB-120037398 | Zbl 1070.20042
[6] Grün O., Beiträge zur Gruppentheorie. I, J. Reine Angew. Math., 1936, 174, 1–14
[7] Iwasawa K., On the structure of infinite M-groups, Japan. J. Math., 1943, 18, 709–728 | Zbl 0061.02504
[8] Kurdachenko L.A., Smith H., Groups in which all subgroups of infinite rank are subnormal, Glasg. Math. J., 2004, 46(1), 83–89 http://dx.doi.org/10.1017/S0017089503001551 | Zbl 1059.20023
[9] Robinson D.J.S., Finiteness Conditions and Generalized Soluble Groups, vols. 1 and 2, Ergeb. Math. Grenzgeb., 62 and 63, Springer, Berlin-Heidelberg-New York, 1972 | Zbl 0243.20032
[10] Robinson D.J.S., A Course in the Theory of Groups, 2nd ed., Grad. Texts in Math., 80, Springer, Berlin-Heidelberg-New York, 1996 http://dx.doi.org/10.1007/978-1-4419-8594-1
[11] Roseblade J.E., On groups in which every subgroup is subnormal, J. Algebra, 1965, 2(4), 402–412 http://dx.doi.org/10.1016/0021-8693(65)90002-5 | Zbl 0135.04901
[12] Schmidt R., Subgroup Lattices of Groups, de Gruyter Exp. Math., 14, Walter de Gruyter, Berlin, 1994 http://dx.doi.org/10.1515/9783110868647
[13] Stonehewer S.E., Permutable subgroups of infinite groups, Math. Z., 1972, 125(1), 1–16 http://dx.doi.org/10.1007/BF01111111 | Zbl 0219.20021