2014/09/30 by Andre Nies, Katrin Tent, Nies, Andre +1
Mathematics · #03B70 #20D99 #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #math.GR #math.LO #msc:03B70 #msc:20D99
paper · pdf · doi:10.48550/arxiv.1409.8390
Glitches in the proofs of Prop 2.2 and Lemma 3.5 have been fixed. Thanks to the people who have noticed. To appear in Israel J. of Mathematics
arxiv created 2016/04/28 · arxiv updated 2016/04/29
We say that a class of finite structures for a finite first-order signature is r-compressible if each structure G in the class has a first-order description of size at most O(r(|G|)). We show that the class of finite simple groups is log-compressible, and the class of all finite groups is log3-compressible. As a corollary we obtain that the class of all finite transitive permutation groups is log3-compressible. The result relies on the classification of finite simple groups, the bi-interpretability of the twisted Ree groups with finite difference fields, the existence of profinite presentations with few relators, and group cohomology. We also indicate why the results are close to optimal.