Essential dimension, stable cohomological dimension, and stable cohomology of finite Heisenberg groups

2014/05/06 by Fedor Bogomolov, Bogomolov, Fedor, Christian Böhning +1
Mathematics · #14E08 #14F43 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14E08 #msc:14F43

paper · pdf · doi:10.48550/arxiv.1405.1394

18 pages

arxiv created 2014/05/06 · arxiv updated 2014/05/07

Abstract

We compare the notions of essential dimension and stable cohomological dimension of a finite group G, prove that the latter is bounded by the length of any normal series with cyclic quotients for G, and show that, however, this bound is not sharp by showing that the stable cohomological dimension of the finite Heisenberg groups H_p, p any prime, is equal to two.

Related

• Minimal dimension of faithful representations for p-groups
• Small Value of cohomological dimension of group homomorphisms
• Sectional rank and Cohomology
• The Virtually Cyclic Classifying Space of the Heisenberg Group
• Essential dimensions of finite groups