Fri Mar 4, 2016
60 Evans Hall, 4:10–6 PM
Katrin Tent (University of Münster)
Describing finite groups by short sentences
We say that a class of finite structures for a finite first-order signature is r-compressible for an unbounded function r : N → N+ 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. 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 for finite groups, and group cohomology.