Complete universal locally finite groups

Ken Hickin
1978 Transactions of the American Mathematical Society  
This paper will partly strengthen a recent application of model theory to the construction of sets of pairwise nonembeddable universal locally finite groups [8] . Our result is Theorem. 77iere is a set % of 2"' universal locally finite groups of order K, with the following properties: 0.1. If U¥= V e % and A and B are uncountable sugroups of V and V, then A and B are not isomorphic. Let A be an uncountable subgroup of U e eIL. 0.2. A does not belong to any proper variety of groups, and 0.3. A
more » ... roups, and 0.3. A is not isomorphic to any of its proper subgroups. 0.4. Every U SQL is a complete group (every automorphism of U is inner).
doi:10.1090/s0002-9947-1978-0480750-4 fatcat:tu23xewhizahrisvcmel5b3epe