Bilinear maps and central extensions of abelian groups

1998/02/13 by Arturo Magidin, Magidin, Arturo
Mathematics · #20E22 #20F18 (Primary) 20J05 (Secondary) #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20E22 #msc:20F18 #msc:20J05

paper · pdf · doi:10.48550/arxiv.math/9802066

16 Pages, Plain TeX

arxiv created 1998/02/13 · arxiv updated 2009/11/30

Abstract

We show that every nilpotent group of class at most two may be embedded in a central extension of abelian groups with bilinear cocycle. The embedding is shown to depend only on the base group. Some refinements are obtained by considering the cohomological situation explicitly.

Related

• Finite p-groups of class 2 as central extensions
• Central Extensions and Cohomology
• Abelian Groups, Homomorphisms and Central Automorphisms of Nilpotent Groups
• Regular Cocycles and Biautomatic Structures
• On Heisenberg groups