On decomposable pseudofree groups

Dirk Scevenels

Type: Article

Publication Date: 1999-01-01

Citations: 0

DOI: https://doi.org/10.1155/s0161171299226178

Abstract

An Abelian group is pseudofree of rank ℓ if it belongs to the extended genus of ℤ ℓ , i.e., its localization at every prime p is isomorphic to . A pseudofree group can be studied through a sequence of rational matrices, the so‐called sequential representation. Here, we use these sequential representations to study the relation between the product of extended genera of free Abelian groups and the extended genus of their direct sum. In particular, using sequential representations, we give a new proof of a result by Baer, stating that two direct sum decompositions into rank one groups of a completely decomposable pseudofree Abelian group are necessarily equivalent. On the other hand, sequential representations can also be used to exhibit examples of pseudofree groups having nonequivalent direct sum decompositions into indecomposable groups. However, since this cannot occur when using the notion of near‐isomorphism rather than isomorphism, we conclude our work by giving a characterization of near‐isomorphism for pseudofree groups in terms of their sequential representations.

Locations

International Journal of Mathematics and Mathematical Sciences - View - PDF
DOAJ (DOAJ: Directory of Open Access Journals) - View

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Works Cited by This (6)

Action	Title	Year	Authors
+	On the genus of a nilpotent group with finite commutator subgroup	1976	Peter Hilton Guido Mislin
+	The genus of a direct product of nilpotent groups of a certain type and non-cancellation phenomena	1995	Dirk Scevenels
+	Nilpotent groups with finite commutator subgroups	1974	Guido Mislin
+	On groups of pseudo-integers	1988	Peter Hilton
+	Calculating the mislin genus for a certain family of nilpotent groups	1991	Carles Casacuberta Peter Hilton
+	Infinite Abelian groups	1970	L. Fuchs