Discriminating and square-like groups
| dc.contributor.author | Belegradek, O | |
| dc.date.accessioned | 2024-07-18T20:49:07Z | |
| dc.date.available | 2024-07-18T20:49:07Z | |
| dc.date.issued | 2004 | |
| dc.department | İstanbul Bilgi Üniversitesi | en_US |
| dc.description.abstract | A group is discriminating if and only if it discriminates its direct square, and square-like if and only if it is universally equivalent to its direct square. It is known that any discriminating group is square-like. These notions were introduced and studied in a series of papers by Baumslag, Myasnikov and Remeslennikov and by Fine, Gaglione, Myasnikov and Spellman. We prove that any square-like group is elementarily equivalent to a countable discriminating group. This answers a question of the second group of authors. We provide an explicit universal - existential axiom system for the class of square-like groups. We show that the theory of the class of discriminating groups is computably enumerable but undecidable. We give a criterion for determining whether a group is discriminating. We propose a construction method for discriminating groups and use it to construct in various group varieties many discriminating non-abelian groups that do not embed their squares. We construct square-like, nondiscriminating nilpotent p-groups of arbitrary nilpotency class; all previously known square-like, non-discriminating groups were abelian. | en_US |
| dc.identifier.doi | 10.1515/jgth.2004.7.4.521 | |
| dc.identifier.endpage | 532 | en_US |
| dc.identifier.issn | 1433-5883 | |
| dc.identifier.issn | 1435-4446 | |
| dc.identifier.issue | 4 | en_US |
| dc.identifier.scopus | 2-s2.0-6344230131 | en_US |
| dc.identifier.scopusquality | Q2 | en_US |
| dc.identifier.startpage | 521 | en_US |
| dc.identifier.uri | https://doi.org/10.1515/jgth.2004.7.4.521 | |
| dc.identifier.uri | https://hdl.handle.net/11411/8094 | |
| dc.identifier.volume | 7 | en_US |
| dc.identifier.wos | WOS:000223773200007 | en_US |
| dc.identifier.wosquality | Q2 | en_US |
| dc.indekslendigikaynak | Web of Science | en_US |
| dc.indekslendigikaynak | Scopus | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Walter De Gruyter Gmbh | en_US |
| dc.relation.ispartof | Journal of Group Theory | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.title | Discriminating and square-like groups | |
| dc.type | Article |
