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On the existence of kappa-existentially closed groups
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10.1007s00013-018-1213-x.pdf
Date
2018-09-01
Author
Kegel, Otto H.
Kaya, Burak
Kuzucuoğlu, Mahmut
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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^{<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
Collections
Department of Mathematics, Article
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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.