kappa-Existentially closed groups

Kegel, Otto H.
Kuzucuoğlu, Mahmut
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.

Citation Formats
O. H. Kegel and M. Kuzucuoğlu, “kappa-Existentially closed groups,” JOURNAL OF ALGEBRA, vol. 499, pp. 298–310, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47026.