DIVISION RINGS ASSOCIATED WITH POLYCYCLIC GROUPS

1987 ◽  
pp. 122-165
Keyword(s):  
Division Rings ◽  
Polycyclic Groups

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

Division Rings Associated with Polycyclic Groups

1984 ◽  
Vol s2-30 (3) ◽  
pp. 465-467
Author(s):  
K. A. Brown ◽  
B. A. F. Wehrfritz
Keyword(s):  
Division Rings ◽  
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?

Polynomials over division rings

1978 ◽  
Vol 31 (3-4) ◽  
pp. 353-358 ◽  
Author(s):  
S. A. Amitsur ◽  
Lance W. Small
Keyword(s):  
Division Rings

scholarly journals Subgroups of finite index in an additive group of a ring

2001 ◽  
Vol 27 (2) ◽  
pp. 83-89
Author(s):  
Doostali Mojdeh ◽  
S. Hassan Hashemi
Keyword(s):  
Finite Index ◽  
Additive Group ◽  
Infinite Field ◽  
Division Rings ◽  
Invertible Elements

IfKis an infinite field andG⫅Kis a subgroup of finite index in an additive group, thenK∗=G∗G∗−1whereG∗denotes the set of all invertible elements inGandG∗−1denotes all inverses of elements ofG∗. Similar results hold for various fields, division rings and rings.

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