Artinian and noetherian factorized groups
Bernhard Amberg (1976)
Rendiconti del Seminario Matematico della Università di Padova
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Bernhard Amberg (1976)
Rendiconti del Seminario Matematico della Università di Padova
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B. Hartley, M. J. Tomkinson (1988)
Rendiconti del Seminario Matematico della Università di Padova
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Leonid Kurdachenko, Javier Otal, Alessio Russo, Giovanni Vincenzi (2011)
Open Mathematics
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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,...
Russo, Francesco (2007)
International Journal of Mathematics and Mathematical Sciences
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Sergio Camp-Mora (2013)
Open Mathematics
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A subgroup H of a group G is called ascendant-by-finite in G if there exists a subgroup K of H such that K is ascendant in G and the index of K in H is finite. It is proved that a locally finite group with every subgroup ascendant-by-finite is locally nilpotent-by-finite. As a consequence, it is shown that the Gruenberg radical has finite index in the whole group.
James C. Beidleman, Howard Smith (1993)
Rendiconti del Seminario Matematico della Università di Padova
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Carlo Casolo (1988)
Rendiconti del Seminario Matematico della Università di Padova
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Leonid Kurdachenko, Howard Smith (2009)
Open Mathematics
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We introduce the notion of the non-subnormal deviation of a group G. If the deviation is 0 then G satisfies the minimal condition for nonsubnormal subgroups, while if the deviation is at most 1 then G satisfies the so-called weak minimal condition for such subgroups (though the converse does not hold). Here we present some results on groups G that are either soluble or locally nilpotent and that have deviation at most 1. For example, a torsion-free locally nilpotent with deviation at...
Leonid A. Kurdachenko, Howard Smith (2005)
Commentationes Mathematicae Universitatis Carolinae
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Let be a group with the property that there are no infinite descending chains of non-subnormal subgroups of for which all successive indices are infinite. The main result is that if is a locally (soluble-by-finite) group with this property then either has subgroups subnormal or is a soluble-by-finite minimax group. This result fills a gap left in an earlier paper by the same authors on groups with the stated property.