منابع مشابه
Absolutely Closed Nil-2 Groups
Using the description of dominions in the variety of nilpotent groups of class at most two, we give a characterization of which groups are absolutely closed in this variety. We use the general result to derive an easier characterization for some subclasses; e.g. an abelian group G is absolutely closed in N2 if and only if G/pG is cyclic for every prime number p . The main result of this paper i...
متن کاملO ct 1 99 8 ABSOLUTELY CLOSED NIL - 2 GROUPS Arturo
Using the description of dominions in the variety of nilpotent groups of class at most two, we give a characterization of which groups are absolutely closed in this variety. We use this to show that a finitely generated abelian group is absolutely closed in N2 if and only if it is cyclic. The main result of this paper is a classification of the absolutely closed groups in the variety N2 (defini...
متن کامل1 1 M ar 1 99 8 Z IS AN ABSOLUTELY CLOSED 2 - NIL GROUP
Using the characterization of dominions in the variety of nilpotent groups of class at most two, we prove that the infinite cyclic group is absolutely closed in this variety. We also conclude from the proof that the same is true of arbitrary cyclic groups. The main result of this paper is that cyclic groups are absolutely closed in the variety N2 (definitions are recalled in Section 1 below). W...
متن کاملRelating the Farrell Nil-groups to the Waldhausen Nil-groups
Every virtually cyclic group Γ that surjects onto the infinite dihedral group D∞ contains an index two subgroup Π of the form H ⋊α Z. We show that the Waldhausen Nil-group of Γ vanishes if and only if the Farrell Nil-group of Π vanishes. 1. Statement of results. The Bass Nil-groups, Farrell Nil-groups, and Waldhausen Nil-groups appear respectively as pieces in the computation of the algebraicK-...
متن کاملAbsolutely Rigid Systems and Absolutely Indecomposable Groups
We give a new proof that there are arbitrarily large indecomposable abelian groups; moreover, the groups constructed are absolutely indecomposable, that is, they remain indecomposable in any generic extension. However, any absolutely rigid family of groups has cardinality less than the partition cardinal κ(ω). Added December 2004: The proofs of Theorems 0.2 and 0.3 are not correct, and the clai...
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ژورنال
عنوان ژورنال: Algebra Universalis
سال: 1999
ISSN: 0002-5240,1420-8911
DOI: 10.1007/s000120050124