On the existence of kappa-existentially closed groups

Date

2018-09-01

Author

Kaya, Burak
Kegel, Otto H.
Kuzucuoğlu, Mahmut

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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We prove that a κ-existentially closed group of cardinality λ exists whenever κ ≤ λ are uncountable cardinals with λ^{&lt;κ} = λ. In particular, we show that there exists a κ-existentially closed group of cardinality κ for regular κ with 2^{&lt;κ} = κ. Moreover, we prove that there exists no κ-existentially closed group of cardinality κ for singular κ. Assuming the generalized continuum hypothesis, we completely determine the cardinals κ ≤ λ for which a κ-existentially closed group of cardinality λ exists<br>

Subject Keywords

Existentially closed groups, Homogeneous groups, Infinite symmetric groups

URI

https://hdl.handle.net/11511/37032

Collections

Department of Mathematics, Article