On products of subgroups in polycyclic groups

1979 ◽  
Vol 33 (1) ◽  
pp. 305-309 ◽  
Author(s):  
John C. Lennox ◽  
John S. Wilson
Keyword(s):  
Products Of Subgroups ◽  
Polycyclic Groups

Primitivity in representations of polycyclic groups

1980 ◽  
Vol 88 (1) ◽  
pp. 15-31 ◽  
Author(s):  
D. L. Harper
Keyword(s):  
Finite Group ◽  
Irreducible Representation ◽  
Nilpotent Group ◽  
Infinite Dimension ◽  
Finitely Generated ◽  
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?

On division rings generated by polycyclic groups

1984 ◽  
Vol 47 (2-3) ◽  
pp. 154-164 ◽  
Author(s):  
B. A. F. Wehrfritz
Keyword(s):  
Division Rings ◽  
Polycyclic Groups

On some polycyclic groups with small Hirsch length

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.

Right-Ordered Polycyclic Groups

1974 ◽  
Vol 17 (2) ◽  
pp. 175-178 ◽  
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.

scholarly journals On the orbit-stabilizer problem for integral matrix actions of polycyclic groups

2003 ◽  
Vol 72 (243) ◽  
pp. 1511-1530 ◽  
Author(s):  
Bettina Eick ◽  
Gretchen Ostheimer
Keyword(s):  
Integral Matrix ◽  
Polycyclic Groups

scholarly journals On a theorem of Rhemtulla on polycyclic groups

2010 ◽  
Vol 214 (10) ◽  
pp. 1898-1900
Author(s):  
B.A.F. Wehrfritz
Keyword(s):  
Polycyclic Groups
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