Akademik Veri Yönetim Sistemi
Monatshefte fur Mathematik, cilt.198, sa.4, ss.791-804, 2022 (SCI-Expanded)
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.We investigate the automorphisms of some κ-existentially closed groups. In particular, we prove that Aut(G) is the union of subgroups of level preserving automorphisms and | Aut(G) | = 2 κ whenever κ is inaccessible and G is the unique κ-existentially closed group of cardinality κ. Indeed, the latter result is a byproduct of an argument showing that, for any uncountable κ and any group G that is the limit of regular representation of length κ with countable base, we have | Aut(G) | = ℶκ+1, where ℶ is the beth function. Such groups are also κ-existentially closed if κ is regular. Both results are obtained by an analysis and classification of level preserving automorphisms of such groups.