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Groups whose all subgroups are ascendant or self-normalizing |
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| Authors: | Leonid A Kurdachenko Javier Otal Alessio Russo Giovanni Vincenzi |
| Institution: | 1. Department of Algebra, National University of Dnepropetrovsk, Dnepropetrovsk, Ukraine 2. Departamento de Matemáticas, Universidad de Zaragoza, Zaragoza, Spain 3. Dipartimento di Matematica, Seconda Università degli studi di Napoli, Caserta, Italy 4. Dipartimento di Matematica e Informatica, Università degli studi di Salerno, Fisciano (Salerno), Italy |
| Abstract: | This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We characterize the structure of such G in case they are locally finite. If G is a hyperabelian group and has the property, we show that every subgroup of G is in fact ascendant provided G is locally nilpotent or non-periodic. We also restrict our study replacing ascendant subgroups by permutable subgroups, which of course are ascendant Stonehewer S.E., Permutable subgroups of infinite groups, Math. Z., 1972, 125(1), 1–16]. |
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