JP Journal of Algebra, Number Theory and Applications
Volume 38, Issue 5, Pages 489 - 497
(October 2016) http://dx.doi.org/10.17654/NT038050489 |
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INFINITE GROUPS WITH TWO CONJUGACY CLASSES OF NON-SUBNORMAL SUBGROUPS
Aifang Feng and Zuhua Liu
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Abstract: Let Gbe an infinite group. mdenotes the number of the conjugacy classes of non-subnormal subgroups of G. and denote the number of the finitely length and infinitely length conjugacy classes of non-subnormal subgroups of G, respectively.
Let Gbe a group with Then it is proved that
(1) there exists no infinite group with
(2) if then there exists some normal subgroup such that is a finite non-nilpotent inner-abelian group, where Nis a group with all subgroups subnormal;
(3) if Gis infinite locally finite, then Gis a Baer group, and |
Keywords and phrases: non-subnormal subgroup, conjugacy class, locally nilpotent, locally finite. |
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