Journal title
Proceedings of the American Mathematical Society
DOI
10.1090/proc/13991
Volume
150
Last updated
2024-04-11T23:44:33.39+01:00
Page
1361-1368
Abstract
Direct powers of perfect groups admit more concise presentations than one might naively suppose. If H1(G;Z) = H2(G;Z) = 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 2 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.
Symplectic ID
736366
Submitted to ORA
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Publication type
Journal Article
Publication date
24 Jan 2022