On groups in which every subgroup of infinite rank is subnormal of bounded defect

Communications in Algebra

Volumn 32, Issue 7, 2004, Pages 2547-2557

  Evans, Martin J ^a   Kim, Youngmi ^b  

^a UNIVERSITY OF ALABAMA   (United States)

^b JACKSONVILLE STATE UNIVERSITY   (United States)

Author keywords

Finite rank; Subnormality

Indexed keywords

EID: 22744435460     PISSN: 00927872     EISSN: None     Source Type: Journal    
DOI: 10.1081/AGB-120037398     Document Type: Article

References (17)

1. Baer, R., Heineken, H. (1972). Radical groups with finite abelian subgroup rank. Illinois J. Math. 16:533-580.
2. Černikov, N. S. (1990). A theorem on groups of finite special rank. Ukrain. Mat. Zh. 42:962-970, English transl. in
3. Ukrainian Math. J. 42 (1990), 855-861.
4. Dixon, M. R., Evans, M. J., Smith, H. (1996). Locally (soluble-by-finite) groups of finite rank. J. Algebra 182:756-769.
5. Dixon, M. R., Evans, M. J., Smith, H. (1999). Locally (soluble-by-finite) groups with all proper non-nilpotent subgroups of finite rank. J. Pure Appl. Algebra 135:33-44.
6. Heineken, H., Mohamed, I. J. (1968). A group with trivial centre satisfying the normalizer condition. J. Algebra 10:368-376.
7. Lennox, J. C., Stonehewer, S. E. (1987). Subnormal Subgroups of Groups. Oxford University Press.
8. Matlis, E. (1958). Injective modules over Noetherian rings. Pacific J. Math. 8: 511-528.
9. Matsumura, H. (1986). Commutative Ring Theory. Cambridge Univ. Press.
10. Menegazzo, F. (1995). Groups of Heineken-Mohamed. J. Algebra 171(3):807-825.
11. Möhres, W. (1990). Auflösbarkeit von Gruppen, deren Untergruppen alle subnormal sind. Arch. Math. 54:232-235.
12. Robinson, D. J. S. (1972). Finiteness Conditions and Generalized Soluble Groups. Vols. 1 and 2.
13. Ergeb. Math. Grenzgeb., Band 62 and 63. Berlin/Heidelberg/New York: Springer-Verlag.
14. Robinson, D. J. S. (1982). A Course in the Theory of Groups. Graduate Texts in Math, 80. Berlin-Heidelburg-New York: Springer-Verlag.
15. Roseblade, J. E. (1965). On groups in which every subgroup is subnormal. J. Algebra 2:402-412.
16. Sharpe, D. W., Vámos, P. (1972). Injective Modules. Cambridge Univ. Press.
17. Smith, H. (2001). Torsion-free groups with all subgroups subnormal. Arch. Math. 76:1-6.