Automorphisms of κ -existentially closed groups

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2022-08-01

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Kaya, Burak
Kuzucuoğlu, Mahmut

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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.

Subject Keywords

Algebraically closed groups, Existentially closed groups

URI

https://hdl.handle.net/11511/98525

Journal

Monatshefte fur Mathematik

DOI

https://doi.org/10.1007/s00605-022-01730-0

Collections

Department of Mathematics, Article

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Citation Formats

B. Kaya and M. Kuzucuoğlu, “Automorphisms of κ -existentially closed groups,” Monatshefte fur Mathematik, vol. 198, no. 4, pp. 791–804, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/98525.