Weak maximality condition and polycyclic groups

In an earlier paper (5) we showed that a finitely generated nilpotent group which is not abelian-by-finite has a primitive irreducible representation of infinite dimension over any non-absolute field. Here we are concerned primarily with the converse question: Suppose that G is a polycyclic-by-finite group with such a representation, then what can be said about G?

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On division rings generated by polycyclic groups

Israel Journal of Mathematics ◽

10.1007/bf02760514 ◽

1984 ◽

Vol 47 (2-3) ◽

pp. 154-164 ◽

Cited By ~ 1

Author(s):

B. A. F. Wehrfritz

Keyword(s):

Division Rings ◽

Polycyclic Groups

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Primitive group algebras of polycyclic groups

Siberian Mathematical Journal ◽

10.1007/bf00967360 ◽

1978 ◽

Vol 19 (1) ◽

pp. 25-30 ◽

Cited By ~ 1

Author(s):

O. I. Domanov

Keyword(s):

Primitive Group ◽

Group Algebras ◽

Polycyclic Groups

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On some polycyclic groups with small Hirsch length

Journal of Algebra and Its Applications ◽

10.1142/s0219498817502371 ◽

2017 ◽

Vol 16 (12) ◽

pp. 1750237

Author(s):

Heguo Liu ◽

Fang Zhou ◽

Tao Xu

Keyword(s):

Abelian Subgroup ◽

Polycyclic Group ◽

Normal Abelian Subgroup ◽

Finite Quotient ◽

Polycyclic Groups

A polycyclic group [Formula: see text] is called an [Formula: see text]-group if every normal abelian subgroup of any finite quotient of [Formula: see text] is generated by [Formula: see text], or fewer, elements and [Formula: see text] is the least integer with this property. In this paper, the structure of [Formula: see text]-groups and [Formula: see text]-groups is determined.

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Computation with Polycyclic Groups

Discrete Mathematics and Its Applications - Handbook of Computational Group Theory ◽

10.1201/9781420035216.ch8 ◽

2005 ◽

pp. 273-324

Keyword(s):

Polycyclic Groups

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Right-Ordered Polycyclic Groups

Canadian Mathematical Bulletin ◽

10.4153/cmb-1974-035-9 ◽

1974 ◽

Vol 17 (2) ◽

pp. 175-178 ◽

Cited By ~ 2

Author(s):

Roberta Botto Mura

Keyword(s):

Additive Group ◽

Real Numbers ◽

Ordered Groups ◽

Polycyclic Groups

One of the features that make right-ordered groups harder to investigate than ordered groups is that their system of convex subgroups may fail to have the following property:(*) if C and C’ are convex subgroups of G and C’ covers C, then C is normal in C’ and C’/C is order-isomorphic to a subgroup of the naturally ordered additive group of real numbers.

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Maximal metric surfaces and the Sobolev-to-Lipschitz property

Calculus of Variations and Partial Differential Equations ◽

10.1007/s00526-020-01843-0 ◽

2020 ◽

Vol 59 (5) ◽

Author(s):

Paul Creutz ◽

Elefterios Soultanis

Keyword(s):

Metric Spaces ◽

Equivalence Classes ◽

Plateau Problem ◽

Lipschitz Property ◽

Maximality Condition ◽

Volume Rigidity

Abstract We find maximal representatives within equivalence classes of metric spheres. For Ahlfors regular spheres these are uniquely characterized by satisfying the seemingly unrelated notions of Sobolev-to-Lipschitz property, or volume rigidity. We also apply our construction to solutions of the Plateau problem in metric spaces and obtain a variant of the associated intrinsic disc studied by Lytchak–Wenger, which satisfies a related maximality condition.

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