Carter subgroups and injectors in a class of locally finite groups
B. Hartley, M. J. Tomkinson (1988)
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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Bernhard Amberg (1976)
Rendiconti del Seminario Matematico della Università di Padova
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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.
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,...
Bernhard Amberg (1983)
Rendiconti del Seminario Matematico della Università di Padova
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Bakić, Radoš (2004)
Novi Sad Journal of Mathematics
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Howard Smith (2011)
Rendiconti del Seminario Matematico della Università di Padova
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Leonid Kurdachenko, Sevgi Atlıhan, Nikolaj Semko (2014)
Open Mathematics
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The main aim of this article is to examine infinite groups whose non-abelian subgroups are subnormal. In this sense we obtain here description of such locally finite groups and, as a consequence we show several results related to such groups.
James Beidleman, Hermann Heineken, Jack Schmidt (2013)
Open Mathematics
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A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on...
M. J. Iranzo, M. Torres (1989)
Rendiconti del Seminario Matematico della Università di Padova
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Bakić, Radoš (1997)
Publications de l'Institut Mathématique. Nouvelle Série
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