caa a22 4500 378894587 CHVBK 20180305123503.0 cr unu---uuuuu 161128e20040906xx s 000 0 eng 10.1515/jgth.2004.7.4.521 doi (NATIONALLICENCE)gruyter-10.1515/jgth.2004.7.4.521 Belegradek Oleg Discriminating and square-like groups [Elektronische Daten] [Oleg Belegradek] 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, non-discriminating nilpotent p-groups of arbitrary nilpotency class; all previously known square-like, non-discriminating groups were abelian. © de Gruyter Mathematical foundations nationallicence Applied mathematics nationallicence Number theory nationallicence Journal of Group Theory Walter de Gruyter 7/4(2004-09-06), 521-532 1433-5883 7:4<521 2004 7 jgth https://doi.org/10.1515/jgth.2004.7.4.521 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/jgth.2004.7.4.521 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Belegradek Oleg NATIONALLICENCE 773 0- Journal of Group Theory Walter de Gruyter 7/4(2004-09-06), 521-532 1433-5883 7:4<521 2004 7 jgth CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter