2017/10/16 by Bridson, Martin R
#20F05 #20J06 #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1710.05904
Direct powers of perfect groups admit more concise presentations than one might naively suppose. If H1G=H2G=0, then Gn has a presentation with O(log n) generators and O(log n)3 relators. If, in addition, there is an element g∈ G that has infinite order in every non-trivial quotient of G, then Gn has a presentation with d(G) +1 generators and O(log n) relators. The bounds that we obtain on the deficiency of Gn are not monotone in n; this points to potential counterexamples for the Relation Gap Problem.