On products of soluble groups of finite rank.

John S. Wilson

Displaying similar documents to “On products of soluble groups 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.

Groups with all subgroups permutable or of finite rank

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.

On the Classification Problem for H-Spaces of Rank Two.

P.J. Hilton, J. Roitberg (1970)

Commentarii mathematici Helvetici

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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.

A note on groups of finite rank

Derek J. S. Robinson (1969)

Compositio Mathematica

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On split $B - N$ pairs of rank 1

Ali Nesin (1990)

Compositio Mathematica

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M₂-rank differences for overpartitions

Jeremy Lovejoy, Robert Osburn (2010)

Acta Arithmetica

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Co-rank and Betti number of a group

Irina Gelbukh (2015)

Czechoslovak Mathematical Journal

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For a finitely generated group, we study the relations between its rank, the maximal rank of its free quotient, called co-rank (inner rank, cut number), and the maximal rank of its free abelian quotient, called the Betti number. We show that any combination of the group's rank, co-rank, and Betti number within obvious constraints is realized for some finitely presented group (for Betti number equal to rank, the group can be chosen torsion-free). In addition, we show that the Betti number...

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.

On 2-Groups with no Abelian Subgroups of Rank Four.

Gernot Stroth (1975)

Mathematische Zeitschrift

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