On the existence of kappa-existentially closed groups

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10.1007s00013-018-1213-x.pdf

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2018-09-01

Author

Kegel, Otto H.
Kaya, Burak
Kuzucuoğlu, Mahmut

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We prove that a κ-existentially closed group of cardinality λ exists whenever κ ≤ λ are uncountable cardinals with λ^{<κ} = λ. In particular, we show that there exists a κ-existentially closed group of cardinalityκ for regular κ with 2^{<κ} = κ. Moreover, we prove that there exists noκ-existentially closed group of cardinality κ for singular κ. Assuming thegeneralized continuum hypothesis, we completely determine the cardinalsκ ≤ λ for which a κ-existentially closed group of cardinality λ exists

Subject Keywords

Existentially closed groups, Homogeneous groups, Infinite symmetric groups

URI

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

Journal

ARCHIV DER MATHEMATIK

DOI

https://doi.org/10.1007/s00013-018-1213-x

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Department of Mathematics, Article

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Citation Formats

O. H. Kegel, B. Kaya, and M. Kuzucuoğlu, “On the existence of kappa-existentially closed groups,” ARCHIV DER MATHEMATIK, pp. 225–229, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37032.