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].
@article{bwmeta1.element.doi-10_2478_s11533-011-0007-1,
author = {Leonid Kurdachenko and Javier Otal and Alessio Russo and Giovanni Vincenzi},
title = {Groups whose all subgroups are ascendant or self-normalizing},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {420-432},
zbl = {1232.20035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0007-1}
}
Leonid Kurdachenko; Javier Otal; Alessio Russo; Giovanni Vincenzi. Groups whose all subgroups are ascendant or self-normalizing. Open Mathematics, Tome 9 (2011) pp. 420-432. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0007-1/
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