Existentially closed locally finite groups

Saharon Shelah

Published 2011-02-28, updated 2015-12-24Version 2

We investigate this class of groups originally called ulf (universal locally finite groups) of cardinality lambda. We prove that for every locally finite group G there is a canonical existentially closed extension of the same cardinality, unique up to isomorphism and increasing with G. Also we get, e.g., existence of complete members (i.e., with no non-inner automorphisms) in many cardinals (provably in ZFC). We also get a parallel to stability theory in the sense of investigating definable types though the class is very unstable.