Abstract: We prove that a periodic residually nilpotent group G all of whose closed subgroups are subnormal is nilpotent. As a particular case, it follows that a periodic residually nilpotent group satisfying the subnormal intersection property is nilpotent.
Residually nilpotent groups whose closed subgroups are subnormal / C. Casolo; A. Martinelli. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 331:(2011), pp. 152-168. [10.1016/j.jalgebra.2010.10.022]
Residually nilpotent groups whose closed subgroups are subnormal
CASOLO, CARLO;MARTINELLI, ALESSANDRO
2011
Abstract
Abstract: We prove that a periodic residually nilpotent group G all of whose closed subgroups are subnormal is nilpotent. As a particular case, it follows that a periodic residually nilpotent group satisfying the subnormal intersection property is nilpotent.
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