Nilpotent Subgroups of Finite Soluble Groups.
John S. Rose (1968)
Mathematische Zeitschrift
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John S. Rose (1968)
Mathematische Zeitschrift
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Abdelhafid Badis, Nadir Trabelsi (2011)
Open Mathematics
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Our main result is that a locally graded group whose proper subgroups are Baer-by-Chernikov is itself Baer-by-Chernikov. We prove also that a locally (soluble-by-finite) group whose proper subgroups are Baer-by-(finite rank) is itself Baer-by-(finite rank) if either it is locally of finite rank but not locally finite or it has no infinite simple images.
Javier Otal, Juan Manuel Peña (1988)
Publicacions Matemàtiques
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This paper deals with one of the ways of studying infinite groups many of whose subgroups have a prescribed property, namely the consideration of minimal conditions. If P is a theoretical property of groups and subgroups, we show that a locally graded group P satisfies the minimal conditions for subgroups not having P if and only if either G is a Cernikov group or every subgroup of G satisfies P, for certain values of P concerning normality, nilpotency and related ideas.
Roger W. Carter (1961)
Mathematische Zeitschrift
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Howard Smith (2011)
Rendiconti del Seminario Matematico della Università di Padova
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Z. Janko, M.F. Newman (1963)
Mathematische Zeitschrift
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B. AMBERG, S. Franciosi, F. Giovanni (1995)
Forum mathematicum
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D. Segal, F.J. Grunewald, G.C. Smith (1988)
Inventiones mathematicae
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Yong Xu, Hailong Hou, Xinjian Zhang (2015)
Open Mathematics
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Using the concept of ɵ-pairs of proper subgroups of a finite group, we obtain some critical conditions of the supersolvability and nilpotency of finite groups.
Artemovych, O. (2002)
Serdica Mathematical Journal
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We characterize the groups which do not have non-trivial perfect sections and such that any strictly descending chain of non-“nilpotent-by-finite” subgroups is finite.
В.В. Блудов, V. V. Bludov, V. V. Bludov, V. V. Bludov (1998)
Algebra i Logika
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Bernhard Amberg (1976)
Rendiconti del Seminario Matematico della Università di Padova
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