Groups with all subgroups permutable or of finite rank

Martyn Dixon; Yalcin Karatas

Displaying similar documents to “Groups with all subgroups permutable or of finite rank”

A note on groups of infinite rank whose proper subgroups are abelian-by-finite

Francesco de Giovanni, Federica Saccomanno (2014)

Colloquium Mathematicae

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It is proved that if G is a locally (soluble-by-finite) group of infinite rank in which every proper subgroup of infinite rank contains an abelian subgroup of finite index, then all proper subgroups of G are abelian-by-finite.

Locally soluble groups with all nontrivial normal subgroups isomorphic.

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.

Groups whose proper subgroups are Baer-by-Chernikov or Baer-by-(finite rank)

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.

A note on groups of finite rank

Derek J. S. Robinson (1969)

Compositio Mathematica

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On a certain purification problem for primary abelian groups

F. Richman, C.P. Walker (1966)

Bulletin de la Société Mathématique de France

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Groups with many nearly normal subgroups

Maria De Falco (2001)

Bollettino dell'Unione Matematica Italiana

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Un sottogruppo $H$ di un gruppo $G$ si dice nearly normal se ha indice finito nella sua chiusura normale $H^{G}$ . In questa nota si caratterizzano i gruppi in cui ogni sottogruppo che non sia nearly normal soddisfa una fissata condizione finitaria $χ$ per diverse scelte naturali della proprietà $χ$ .

On products of soluble groups of finite rank.

John S. Wilson (1985)

Commentarii mathematici Helvetici

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Groups with small deviation for non-subnormal subgroups

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...

Groups with finitely many conjugacy classes of non-normal subgroups of infinite rank

Maria De Falco, Francesco de Giovanni, Carmela Musella (2013)

Colloquium Mathematicae

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It is proved that if a locally soluble group of infinite rank has only finitely many non-trivial conjugacy classes of subgroups of infinite rank, then all its subgroups are normal.

Groups with the weak minimal condition for non-subnormal subgroups II

Leonid A. Kurdachenko, Howard Smith (2005)

Commentationes Mathematicae Universitatis Carolinae

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Let $G$ be a group with the property that there are no infinite descending chains of non-subnormal subgroups of $G$ for which all successive indices are infinite. The main result is that if $G$ is a locally (soluble-by-finite) group with this property then either $G$ has subgroups subnormal or $G$ 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.