2010/02/12 by Mohsen Parvizi, Behrooz Mashayekhy
Engineering · Mathematics · #Abelian group #Commutator #Commutator subgroup #Elementary abelian group #Finitely-generated abelian group #Invariant (physics) #Limits and Structures in Graph Theory #Multiplier (economics) #Rank of an abelian group #Rings, Modules, and Algebras #Stallings theorem about ends of groups #graph theory and CDMA systems #math.GR #msc:20E10 #msc:20E34 #msc:20F12 #msc:20F18
paper · pdf · doi:10.1080/00927870902828587
published as Communications in Algebra, 38: 588-600, 2010 · 19 pages
openalex publication_date 2010/02/12 · arxiv created 2010/12/15 · arxiv updated 2015/11/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present an explicit structure for the Baer invariant of a finitely generated abelian group with respect to the variety [𝔑 c 1 , 𝔑 c 2 ], for all c 2 ≤ c 1 ≤ 2c 2. As a consequence, we determine necessary and sufficient conditions for such groups to be [𝔑 c 1 , 𝔑 c 2 ]-capable. We also show that if c 1 ≠ 1 ≠ c 2, then a finitely generated abelian group is [𝔑 c 1 , 𝔑 c 2 ]-capable if and only if it is capable. Finally, we show that 𝔖2-capability implies capability, but there is a capable finitely generated abelian group which is not 𝔖2-capable.