Summary
We characterize the groups given in the title in the case of locally finite, locally nilpotent and radical groups.
Sunto
I gruppi con tutti i sottogruppi nonfinitamente generati subnormali sono caratterizzati nella classe dei gruppi localmente finiti, localmente nilpotenti e radicali.
Article PDF
Similar content being viewed by others
References
S. N. Chernikov,Groups with prescribed properties for systems of infinite subgroups, Ukrain. Mat. Ž.,19 (6) (1967), pp. 111–131.
P.Hall,Nilpotent Groups, Collected Works of Philipp Hall, Oxford (1988).
B. Hartley -M. J. Romkinson,Splitting nilpotent and hypercentral residuals, Math. Proc. Cambridge Phil. Soc.,78 (1975), pp. 215–226.
B. Hartley,A dual approach to Černikov modules, Math. Proc. Cambridge Phil. Soc.,82 (1977), pp. 215–239.
H. Heineken -I. J. Mohamed,A group with trivial centre satisfying the normalizer condition, J. Algebra,10 (1968), pp. 368–376.
M. J.Kargapolov - Yu. J.Merzlyakov,Fundamental of Group Theory, Moscow (1982) (Russian).
O. H.Kegel - B. A. F.Wehrfritz,Locally Finite Groups, Amsterdam (1973).
L. A. Kurdachenko,FC-groups for which the set of orders of the elements of the periodic part is bounded, Sib. Math. Ž.,16 (6) (1975), pp. 1205–1213 (Russian).
J. C.Lennox - S. E.Stonehewer,Subnormal Subgroups of Groups, Oxford (1987).
W. Möhres,Torsionsfreie Gruppen, deren Untergruppen alle subnormal sind, Math. Annalen,204 (1989), pp. 245–249.
W. Möhres,Auflösbare Gruppen mit endlichen Exponenten, deren Untergruppen alle subnormal sind, Rend. Sem. Mat. Univ. Padova,81 (1989), pp. 269–287.
W. Möhres,Auflösbarkeit von Gruppen, deren Untergruppen alle subnormal sind, Arkiv der Mathematik,54 (1990), pp. 232–235.
D. S.Passmann,The Algebraic Structure of Group Rings, New York (1977).
R. E. Phillips,Infinite groups with normality condition on infinite subgroups, Rocky Mountains J. Math.,7 (1977), pp. 19–30.
B. I. Plotkin,Radical groups, Mat. Sb.,37 (79) (1955), pp. 507–526.
D. J. S.Robinson,Finiteness Conditions and Generalized Soluble Groups I, Berlin, Göttingen, Heidelberg (1972).
D. J. S.Robinson,Finiteness Conditions and Generalized Soluble Groups II, Berlin, Göttingen, Heidelberg (1972).
D. J. S.Robinson,A Course in the Theory of Groups, Berlin, Göttingen, Heidelberg (1982).
J. E. Roseblade,On groups in which every subgroup is subnormal, J. Algebra,2 (1965), pp. 402–412.
S. E. Stonehewer,Nilpotent residuals of subnormal subgroups, Math. Z.,139 (1974), pp. 45–54.
B. A. F.Wehrfritz,Infinite Linear Groups, Berlin. Heidelberg, New York (1973).
D. J. Zaicev,Complementation of subgroups of external groups, inInvestigations of Groups with Prescribed Properties of Subgroups, Inst. Mat. Akad. Nauk Ukrain. SSR. Kiev (1974), pp. 72–130 (Russian).
D. J. Zaicev,On locally soluble groups of finite rank, Doklay A.N. SSSR,240 (2) (1978), pp. 257–259 (Russian).
D. J. Zaicev,On the properties of groups inherited by their normal subgroups, Ukrain. Mat. Sb.,38 (1986), pp. 707–713 (Russian).
Author information
Authors and Affiliations
Additional information
This work was carried out while the second author visited the University of Würzburg with the aid of Deutsche Forschungsgemeinschaft (DFG). The second author is grateful to DFG for making this visit possible and to Mathematisches Institut Würzburg for the hospitality he enjoyed.
Rights and permissions
About this article
Cite this article
Heineken, H., Kurdachenko, L.A. Groups with subnormality for all subgroups that are not finitely generated. Annali di Matematica pura ed applicata 169, 203–232 (1995). https://doi.org/10.1007/BF01759354
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01759354