The Primitivity of Group Rings of Soluble Groups with Trivial Periodic Radical

1985 ◽  
Vol s2-31 (1) ◽  
pp. 41-47
Author(s):  
C. J. B. Brookes
Keyword(s):  
Group Rings ◽  
Soluble Groups

More soluble groups with primitive group rings

1983 ◽  
Vol 41 (1) ◽  
pp. 1-4
Author(s):  
C. J. B. Brookes
Keyword(s):  
Primitive Group ◽  
Group Rings ◽  
Soluble Groups

ON MODULES OVER GROUP RINGS OF LOCALLY SOLUBLE GROUPS WITH RANK RESTRICTIONS ON SOME SYSTEMS OF SUBGROUPS

2010 ◽  
Vol 03 (01) ◽  
pp. 45-55 ◽  
Author(s):  
O. Yu. Dashkova
Keyword(s):  
Soluble Group ◽  
Proper Subgroup ◽  
Dedekind Domain ◽  
Group Rings ◽  
Soluble Groups ◽  
Rank Restrictions ◽  
Locally Soluble Group ◽  
Dg Module

We consider a DG-module A over a Dedekind domain D. Let G be a group having infinite section p-rank (or infinite 0-rank) such that CG(A) = 1. It is known that if A is not an artinian D-module then for every proper subgroup H, the quotient A/CA(H) is an artinian D-module for every proper subgroup H of infinite section p-rank (or infinite 0-rank respectively). In this paper, it is proved that if G is a locally soluble group, then G is soluble. Some properties of soluble groups of this type are also obtained.

On groups with countably many maximal subgroups

2018 ◽  
Vol 21 (2) ◽  
pp. 253-271 ◽  
Author(s):  
Ahmet Arikan ◽  
Giovanni Cutolo ◽  
Derek J. S. Robinson
Keyword(s):  
Maximal Subgroups ◽  
Group Rings ◽  
Soluble Groups

AbstractThe object of this work is to find classes of groups which possess only countably many maximal subgroups. Modules with countably many maximal submodules and group rings having countably many maximal right ideals are also investigated. Examples of soluble groups with uncountably many maximal subgroups are described.

Primitive group rings of soluble groups

1981 ◽  
Vol 36 (1) ◽  
pp. 404-413 ◽  
Author(s):  
Kenneth A. Brown
Keyword(s):  
Primitive Group ◽  
Group Rings ◽  
Soluble Groups

Ideals in group rings of soluble groups of finite rank

1985 ◽  
Vol 97 (1) ◽  
pp. 27-49 ◽  
Author(s):  
Christopher J. B. Brookes
Keyword(s):  
Finite Rank ◽  
Prime Ideals ◽  
Group Rings ◽  
Soluble Groups ◽  
Original Motivation

The original motivation for this paper was the question of primitivity for group rings of soluble groups of finite rank. At the end this is touched upon as an application of a theorem about prime ideals in such rings. If a group Γ acts on a set S we say an element is (Γ)-orbital if its orbit is finite and write ΔΓ(S) for the subset of such elements. The FC-radical of a group G, denoted by Δ(G), is just ΔG(G) where the action of G on itself is by conjugation.

Soluble groups with coherent group rings

1979 ◽  
pp. 235-240 ◽  
Author(s):  
Robert Bieri ◽  
Ralph Strebel
Keyword(s):  
Group Rings ◽  
Soluble Groups
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