Groups with all subgroups permutable or of finite rank

Central European Journal of Mathematics

Volumn 10, Issue 3, 2012, Pages 950-957

  Dixon, Martyn R ^a   Karatas, Yalcin ^a  

^a UNIVERSITY OF ALABAMA   (United States)

Author keywords

Finite rank; Locally nilpotent; Permutable subgroup

Indexed keywords

EID: 84859158061     PISSN: 18951074     EISSN: 16443616     Source Type: Journal    
DOI: 10.2478/s11533-012-0012-z     Document Type: Article

References (13)

1. Baer R., Heineken H., Radical groups of finite abelian subgroup rank, Illinois J. Math., 1972, 16(4), 533-580.
2. Chernikov N. S., A theorem on groups of finite special rank, Ukrainian Math. J., 1990, 42(7), 855-861.
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.
4. Dixon M. R., Evans M. J., Smith H., Locally (soluble-by-finite) groups of finite rank, J. Algebra, 1996, 182(3), 756-769.
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.
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.
8. Kurdachenko L. A., Smith H., Groups in which all subgroups of infinite rank are subnormal, Glasg. Math. J., 2004, 46(1), 83-89.
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.
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.
11. Roseblade J. E., On groups in which every subgroup is subnormal, J. Algebra, 1965, 2(4), 402-412.
12. Schmidt R., Subgroup Lattices of Groups, de Gruyter Exp. Math., 14, Walter de Gruyter, Berlin, 1994.
13. Stonehewer S. E., Permutable subgroups of infinite groups, Math. Z., 1972, 125(1), 1-16.