Discriminating and square-like groups
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| 024 | 7 | 0 | |a 10.1515/jgth.2004.7.4.521 |2 doi |
| 035 | |a (NATIONALLICENCE)gruyter-10.1515/jgth.2004.7.4.521 | ||
| 100 | 1 | |a Belegradek |D Oleg | |
| 245 | 1 | 0 | |a Discriminating and square-like groups |h [Elektronische Daten] |c [Oleg Belegradek] |
| 520 | 3 | |a 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. | |
| 540 | |a © de Gruyter | ||
| 690 | 7 | |a Mathematical foundations |2 nationallicence | |
| 690 | 7 | |a Applied mathematics |2 nationallicence | |
| 690 | 7 | |a Number theory |2 nationallicence | |
| 773 | 0 | |t Journal of Group Theory |d Walter de Gruyter |g 7/4(2004-09-06), 521-532 |x 1433-5883 |q 7:4<521 |1 2004 |2 7 |o jgth | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/jgth.2004.7.4.521 |q text/html |z Onlinezugriff via DOI |
| 908 | |D 1 |a research article |2 jats | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1515/jgth.2004.7.4.521 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Belegradek |D Oleg | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Group Theory |d Walter de Gruyter |g 7/4(2004-09-06), 521-532 |x 1433-5883 |q 7:4<521 |1 2004 |2 7 |o jgth | ||
| 900 | 7 | |b CC0 |u http://creativecommons.org/publicdomain/zero/1.0 |2 nationallicence | |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-gruyter | ||