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kappa-Existentially closed groups
Date
2018-04-01
Author
Kegel, Otto H.
Kuzucuoğlu, Mahmut
Metadata
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This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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Let kappa is be an infinite cardinal. The class of kappa-existentially closed groups is defined and their basic properties are studied. Moreover, for an uncountable cardinal kappa, uniqueness of kappa-existentially closed groups are shown, provided that they exist. We also show that for each regular strong limit cardinal kappa, there exists kappa-existentially closed groups. The structure of centralizers of subgroups of order less than kappa in a kappa-existentially group G are determined up to isomorphism namely, for any subgroup F <= G(nu) in G with vertical bar F vertical bar < kappa, the subgroup C-G(F) is isomorphic to an extension of Z(F) by G.
Subject Keywords
Infinite symmetric groups
,
Centralizers of subgroups
,
Existentially closed groups
,
Universal groups
URI
https://hdl.handle.net/11511/47026
Journal
JOURNAL OF ALGEBRA
DOI
https://doi.org/10.1016/j.jalgebra.2017.12.005
Collections
Department of Mathematics, Article