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The present paper generalizes their work to obtain similar results for infinite subgroups of the group of unimodular complex numbers. Furthermore, the groups which satisfy the same first\u2010order sentences as ultraproducts of finite cyclic groups are\u00a0characterized.<\/jats:p>","DOI":"10.1002\/malq.201600037","type":"journal-article","created":{"date-parts":[[2019,12,11]],"date-time":"2019-12-11T14:18:27Z","timestamp":1576073907000},"page":"412-443","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Pseudo\u2010c\u2010archimedean and pseudo\u2010finite cyclically ordered groups"],"prefix":"10.1002","volume":"65","author":[{"given":"G\u00e9rard","family":"Leloup","sequence":"first","affiliation":[{"name":"Laboratoire Manceau de Math\u00e9matiques, Facult\u00e9 des Sciences Le Mans Universit\u00e9 avenue Olivier Messiaen 72085 Le Mans Cedex 9 France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2019,12,11]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.2307\/1970573"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.2307\/2373065"},{"key":"e_1_2_7_4_1","volume-title":"Model Theory","author":"Chang C. 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