Finitely-generated abelian group
Rational points on smooth cubic hypersurfaces
... been possible without the use of Algebraic Geometry in Number Theory. A finer categorisation for curves is the genus. Curves are far more studied and understood than higher dimensional varieties, but even in this case, ...
100
On Semiabelian Groups
... a finitely generated semiabelian ...nilpotent finitely gen- erated group, its periodic part t(G) is also finitely generated (see, ...is finitely generated, the ...
6
Endotrivial modules in the cyclic case
... The group T (G) is called the group of endotrivial ...a finitely generated abelian ...finite group, as we shall see in the main ...
6
Finitely generated left ideals in Banach algebras on groups and semigroups
... a is holomorphic on U under this identification for every a ∈ A. Does it then follow that the maximal ideals corresponding to points of U are finitely-generated? T. T. Reed gave an example [16, Example ...
36
Groups with many pronormal and transitively normal subgroups
... arbitrary finitely generated subgroup of L/A. Since every finitely generated subgroup of locally nilpotent group is polycyclic, F is not finitely ...not finitely ...
18
Commutator Length of Finitely Generated Linear Groups
... a group G is the least natural number c such that every element of the derived subgroup of G is a product of c ...linear group over C that depends only on d and the degree of ...a group G, we prove ...
5
Relatively hyperbolic groups
... torus group is an example of a geometrically finite kleinian ...the group is hyperbolic relative to the maximal parabolic subgroups, which in this situation are always finitely generated ...
63
Groups with many pronormal and transitively normal subgroups
... Dedekind group. In particular, every subgroup of G, which is non-finitely generated, is normal in ...is abelian or finitely ...hypercentral group satisfies the normalizer ...
23
Groups with poly context free word problem
... every finitely generated torsion-free soluble group that is not virtually abelian has a subgroup isomorphic to either Z ∞ or a proper ...every finitely generated soluble ...
120
Presentations for subsemigroups of groups
... free group and a polycyclic group is Malcev ...free group and an abelian group is M alcev ...non-automatic finitely generated subsemigroup of the direct product of a free ...
200
On the existence of complements in a group to some abelian normal subgroups
... soluble group of finite Hirsch-Zaitsev ...with abelian factors. Clearly, a soluble–by–finite minimax group has a finite ...a group G is said to have finite special rank r(G) = r if every ...
24
Some groups of finite homological type
... The group G is said to be of finite homological type or F HT if G has finite virtual cohomological dimension, and for every G-module M whose underlying abelian group is finitely ...
11
Product of Soluble Minimax Groups
... an abelian normal section U/V which is either torsion- free or periodic and is not finitely ...an abelian normal subgroup of G which is either torsion-free or ...the group G satisfies the ...
6
On almost finitely generated nilpotent groups
... In the category of abelian groups a subgroup of an fg-like group is fg-like, ii an extension of an fg-like group by an fg-like group is fg-like We thus devote much attention to the statu[r] ...
6
Periodic rings with finitely generated underlying group
... finitely generated un- derlying abelian group reduces to knowing the finite rings, the periodic rings which are free of finite rank as groups, and computing some ring ...
6
Automorphisms fixing subnormal subgroups of certain infinite soluble groups
... ABELIAN-BY-NILPOTENT GROUPS Recall from Chapter 5 our main result Theorem E, that if G is a finitely generated infinite metabelian group, then the group Autsn G is a finite Abelian group[r] ...
92
On generators and presentations of semidirect products in inverse semigroups
... Investigation of finite generation and finite presentability of various constructions is one of the main areas of research in combinatorial semigroup theory. For example, finite generation and presentability of direct ...
13
Generators and relations for subsemigroups via boundaries in Cayley graphs
... a group shares many of its properties with its subgroups of finite ...of finitely presented groups with finite index are finitely presented; see [18, Proposition ...of finitely presented ...
36
Finitely Generated Annihilating-Ideal Graph of Commutative Rings
... Let R be a commutative ring and A (R) be the set of all ideals with non-zero annihilators. Assume that A ∗ (R) = A (R) ⧹{ (0) } and F (R) denote the set of all finitely generated ideals of R. In this paper, ...
9
Modules whose maximal submodules have \(\tau\)-supplements
... Throughout this paper, we assume that all rings are associative with iden- tity and all modules are unital left modules. For a module M, by N ⊆ M we shall mean that N is a submodule of M . A submodule N ⊆ M is called ...
9