Simple groups separated by finiteness properties
Skipper, Rachel
Skipper
Rachel
Witzel, Stefan
Witzel
Stefan
Zaremsky, Matthew C. B.
Zaremsky
Matthew C. B.
We show that for every positive integer n there exists a simple group that is of type Fn-1 but not of type Fn. For n3 these groups are the first known examples of this kind. They also provide infinitely many quasi-isometry classes of finitely presented simple groups. The only previously known infinite family of such classes, due to Caprace-Remy, consists of non-affine Kac-Moody groups over finite fields. Our examples arise from Rover-Nekrashevych groups, and contain free abelian groups of infinite rank.
215
2
713-740
713-740
Springer
2019