Title of article :
On some groups whose subnormal subgroups are contranormal-free
Author/Authors :
Kurdachenko ، Leonid A. Department of Algebra and Geometry - School of Mathematics and Mechanics - National Dnipro University , Longobardi ، Patrizia Department of Mathematics - Università di Salerno , Maj ، Mercede Department of Mathematics - Università di Salerno
From page :
99
To page :
115
Abstract :
If G is a group, a subgroup H of G is said to be contranormal in G if HG = G, where HG is the normal closure of H in G. We say that a group is contranormal-free if it does not contain proper contranormal subgroups. Obviously, a nilpotent group is contranormal-free. Conversely, if G is a finite contranormal-free group, then G is nilpotent. We study (infinite) groups whose subnormal subgroups are contranormal-free. We prove that if G is a group which contains a normal nilpotent subgroup A such that G/A is a periodic Baer group, and every subnormal subgroup of G is contranormal-free, then G is generated by subnormal nilpotent subgroups; in particular G is a Baer group. Furthermore, if G is a group which contains a normal nilpotent subgroup A such that the 0-rank of A is finite, the set Π(A) is finite, G/A is a Baer group, and every subnormal subgroup of G is contranormal-free, then G is a Baer group.
Keywords :
Contranormal subgroups , subnormal subgroups , nilpotent groups , hypercentral groups , upper central series
Journal title :
International Journal of Group Theory
Journal title :
International Journal of Group Theory
Record number :
2781535
Link To Document :
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