John C. Lennox, Howard Smith, James Wiegold (1994)
Publicacions Matemàtiques
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Let G be an infinite, locally soluble group which is isomorphic to all its nontrivial normal subgroups. If G/G' has finite p-rank for p = 0 and for all primes p, then G is cyclic.
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.
John C. Lennox, Derek J. S. Robinson (1980)
Rendiconti del Seminario Matematico della Università di Padova
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John C. Lennox (1996)
Rendiconti del Seminario Matematico della Università di Padova
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Martyn Dixon, Yalcin Karatas (2012)
Open Mathematics
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In this paper we investigate the structure of X-groups in which every subgroup is permutable or of finite rank. We show that every subgroup of such a group is permutable.
Sanati, Mahboubeh Alizadeh (2008)
International Journal of Mathematics and Mathematical Sciences
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Patrizia Longobardi, Mercede Maj (1993)
Rendiconti del Seminario Matematico della Università di Padova
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Silvana Franciosi, Francesco de Giovanni (1995)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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It is proved that a soluble residually finite minimax group is finite-by-nilpotent if and only if it has only finitely many maximal subgroups which are not normal.
Howard Smith (1983)
Mathematische Zeitschrift
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