Third Conference and Workshop on Group theory , 2011-03-09

#### Title : ( An Outer Commutator Capability of Finitely Generated Abelian Groups )

Authors: Mohsen Parvizi , Behrooz Mashayekhy Fard ,

Citation: BibTeX | EndNote

#### Abstract

We use the explicit structure for the Baer invariant of a finitely generated abelian group with respect to the variety $[\\\\mathfrak{N}_{c_1},\\\\mathfrak{N}_{c_2}]$, for all $c_2\\\\leq c_1\\\\leq 2c_2$, to determine necessary and sufficient conditions for such groups to be $[\\\\mathfrak{N}_{c_1},\\\\mathfrak{N}_{c_2}]$-capable. We also show that if $c_1\\\\neq 1\\\\neq c_2$, then a finitely generated abelian group is $[\\\\mathfrak{N}_{c_1},\\\\mathfrak{N}_{c_2}]$-capable if and only if it is capable.

#### Keywords

Capability; Outer commutator variety; Finitely generated abelian groups
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@inproceedings{paperid:1027600,
author = {Parvizi, Mohsen and Mashayekhy Fard, Behrooz},
title = {An Outer Commutator Capability of Finitely Generated Abelian Groups},
booktitle = {Third Conference and Workshop on Group theory},
year = {2011},
location = {تهران, IRAN},
keywords = {Capability; Outer commutator variety; Finitely generated abelian groups},
}