JP Journal of Algebra, Number Theory and Applications
Volume 29, Issue 1, Pages 83 - 90
(May 2013)
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INFINITE GROUPS WITH ONE CONJUGATE CLASS OF NON-SUBNORMAL SUBGROUPS
Zuhua Liu and Aifang Feng
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Abstract: Let Gbe an infinite group with one conjugate class of non-subnormal subgroups. It is shown that the following are equivalent: Gis locally nilpotent; Gsatisfies the normalizer condition; Gis a Baer group. If G is a group with the given property, then Gneeds not be locally finite. If Gis an inner finite group, then Gis an extension of the center by a Tarski p-group. Moreover, Gis a simple inner finite group with the given property if and only if Gis a Tarski p-group. |
Keywords and phrases: locally nilpotent, non-subnormal subgroup, conjugate, locally finite, inner-finite. |
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