kappa-Existentially closed groups

Kegel O. H., KUZUCUOĞLU M.

JOURNAL OF ALGEBRA, vol.499, pp.298-310, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 499
  • Publication Date: 2018
  • Doi Number: 10.1016/j.jalgebra.2017.12.005
  • Journal Name: JOURNAL OF ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.298-310
  • Keywords: Infinite symmetric groups, Universal groups, Centralizers of subgroups, Existentially closed groups
  • Middle East Technical University Affiliated: Yes

Abstract

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. (C) 2017 Elsevier Inc. All rights reserved.