Splitting length of abelian mixed groups of torsion-free rank 1

2009 ◽  
Vol 164 (2) ◽  
pp. 294-302
Author(s):  
Pham Thi Thu Thuy
Keyword(s):  
Free Rank ◽  
Mixed Groups ◽  
Torsion Free Rank ◽  
Torsion Free

QUASI-ISOMORPHISMS AND GROUPS OF QUASI-HOMOMORPHISMS

2009 ◽  
Vol 08 (05) ◽  
pp. 617-627
Author(s):  
ULRICH ALBRECHT ◽  
SIMION BREAZ
Keyword(s):  
Abelian Group ◽  
Dual Problem ◽  
Abelian Groups ◽  
Mixed Abelian Group ◽  
Free Rank ◽  
Mixed Groups ◽  
Torsion Free Rank ◽  
Torsion Free

This paper investigates to which extent a self-small mixed Abelian group G of finite torsion-free rank is determined by the groups Hom (G,C) where C is chosen from a suitable class [Formula: see text] of Abelian groups. We show that G is determined up to quasi-isomorphism if [Formula: see text] is the class of all self-small mixed groups C with r0(C) ≤ r0(G). Several related results are given, and the dual problem of orthogonal classes is investigated.

Splitting Mixed Groups of Finite Torsion-Free Rank

2004 ◽  
Vol 32 (4) ◽  
pp. 1587-1601 ◽  
Author(s):  
Takashi Okuyama
Keyword(s):  
Free Rank ◽  
Mixed Groups ◽  
Torsion Free Rank ◽  
Torsion Free

GENERALIZED ENDOPRIMAL ABELIAN GROUPS

2006 ◽  
Vol 05 (01) ◽  
pp. 1-17 ◽  
Author(s):  
U. ALBRECHT ◽  
S. BREAZ ◽  
W. WICKLESS
Keyword(s):  
Abelian Group ◽  
Simple Form ◽  
Abelian Groups ◽  
Free Rank ◽  
Torsion Groups ◽  
Mixed Groups ◽  
Torsion Free Rank ◽  
Torsion Free ◽  
Nil Radical ◽  
Natural Way

An n-ary endofunction on an abelian group G is a function f : Gn → G such that f(θg1,…,θgn) = θ f(g1,…,gn) for all endomorphisms θ of G. A group G is endoprimal if, for each natural number n, each n-ary endofunction has the following simple form: [Formula: see text] for some collection of integers {li : 1 ≤ i ≤ n}. The notion of endoprimality arises from universal algebra in a natural way and has been applied to the study of abelian groups in papers Davey and Pitkethly (97), Kaarli and Marki (99) and Göbel, Kaarli, Marki, and Wallutis (to appear). These papers make the case that the notion of endoprimality can give rise to interesting and tractable classes of abelian groups. We continue working along these lines, adapting our definition to make it more suitable for working with general classes of abelian groups. We study generalized endoprimal (ge) abelian groups. Here every n-ary endofunction is required to be of the form [Formula: see text] for some collection of central endomorphisms {λi : 1 ≤ i ≤ n} of G. (Note that such a sum is always an endofunction.) We characterize generalized endoprimal abelian groups in a number of cases, in particular for torsion groups, torsion-free finite rank groups G such that E(G) has zero nil radical, and self-small mixed groups of finite torsion-free rank.

scholarly journals On mixed groups of torsion-free rank one

1967 ◽  
Vol 11 (1) ◽  
pp. 134-144 ◽  
Author(s):  
Charles K. Megibben
Keyword(s):  
Rank One ◽  
Free Rank ◽  
Mixed Groups ◽  
Torsion Free Rank ◽  
Torsion Free

On the Square Subgroup of a Mixed SI-Group

2018 ◽  
Vol 61 (1) ◽  
pp. 295-304 ◽  
Author(s):  
R. R. Andruszkiewicz ◽  
M. Woronowicz
Keyword(s):  
Abelian Group ◽  
Quotient Group ◽  
Abelian Groups ◽  
Additive Group ◽  
Negative Solution ◽  
New Class ◽  
Free Rank ◽  
Torsion Free Rank ◽  
Torsion Free ◽  
Group Modulo

AbstractThe relation between the structure of a ring and the structure of its additive group is studied in the context of some recent results in additive groups of mixed rings. Namely, the notion of the square subgroup of an abelian group, which is a generalization of the concept of nil-group, is considered mainly for mixed non-splitting abelian groups which are the additive groups only of rings whose all subrings are ideals. A non-trivial construction of such a group of finite torsion-free rank no less than two, for which the quotient group modulo the square subgroup is not a nil-group, is given. In particular, a new class of abelian group for which an old problem posed by Stratton and Webb has a negative solution, is indicated. A new, far from obvious, application of rings in which the relation of being an ideal is transitive, is obtained.

scholarly journals The torsion-free rank of homology in towers of soluble pro-p groups

2017 ◽  
Vol 219 (2) ◽  
pp. 817-834 ◽  
Author(s):  
Martin R. Bridson ◽  
Dessislava H. Kochloukova
Keyword(s):  
Free Rank ◽  
Torsion Free Rank ◽  
Torsion Free
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