kappa-Existentially closed groups

Date

2018-04-01

Author

Kegel, Otto H.
Kuzucuoğlu, Mahmut

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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

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Citation Formats

O. H. Kegel and M. Kuzucuoğlu, “kappa-Existentially closed groups,” JOURNAL OF ALGEBRA, pp. 298–310, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47026.