The divisible radical of a group
Tóm tắt
We consider the existence or otherwise of canonical divisible normal subgroups of groups in general. We present more counterexamples than positive results. These counterexamples constitute the substantive part of this paper.
Tài liệu tham khảo
Fuchs L., Infinite Abelian Groups Vol. 1, Academic Press, New York, 1970
Hall P., Nilpotent Groups, Queen Mary College Math. Notes, London, 1969
Jacobson N., The Theory of Fields, Van Nostrand, New York, 1964
Robinson D.J.S., Finiteness Conditions and Generalized Soluble Groups, Springer-Verlag, Berlin, 1972
Wehrfritz B.A.F., On hypercentral groups, Cent. Eur. J. Math., 2007, 5, 596–606
Wehrfritz B.A.F., The abelianization of hypercyclic groups, Cent. Eur. J. Math., 2007, 5, 686–695
Wehrfritz B.A.F., On hyper (abelian of finite rank) groups, Algebra Colloq., 2008, 15, 361–370
Wehrfritz B.A.F., On hyper and hypo abelian-of-finite-rank groups, Asian-Europ. J. Math., 2008, 1, 431–438