Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

ON SUBCLASSES OF GROUPS WITHOUT FREE SUBSEMIGROUPS

ON SUBCLASSES OF GROUPS WITHOUT FREE SUBSEMIGROUPS DEMONSTRATIO MATHEMATICAVol. XXXIIINo 12000B. Bajorska, O. MacedoriskaON SUBCLASSES OF GROUPSW I T H O U T FREE SUBSEMIGROUPSAbstract. The paper is inspired by the question of A. Shalev about possible coincidence of the class of collapsing groups and groups satisfying positive laws. We split theclass of collapsing groups for subclasses, corresponding to different functions on naturalnumbers and give a positive answer for some of them.1. IntroductionLet Ti be a free semigroup generated by x, y and let u(x, y), v(x, y) € Ti.By a (positive) law of degree n we mean here a binary expression(1)u(x,y) = v(x,y),where x (and y) has the same exponent sum on both sides; the first (andthe last) letters in u and v are different; the length of u (equal to the lengthof v) is n. From now on by a pair of elements we mean an ordered one. Wesay that a pair g, h of elements in a group satisfies a law (1) if the equalityu(g, h) = v(g, h) holds. A subset satisfies a law (1) if every pair of elementsin the subset does.Many authors considered properties of groups, which do not containnon-abelian free subsemigroups or, which is the same, groups with no http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ON SUBCLASSES OF GROUPS WITHOUT FREE SUBSEMIGROUPS

Bajorska, B.; Macedońska, O.
Demonstratio Mathematica , Volume 33 (1): 8 – Jan 1, 2000
Download PDF
8 pages

Loading next page...
 
/lp/de-gruyter/on-subclasses-of-groups-without-free-subsemigroups-s21iPM0XRd

References (12)

Publisher
de Gruyter
Copyright
© by B. Bajorska
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2000-0105
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XXXIIINo 12000B. Bajorska, O. MacedoriskaON SUBCLASSES OF GROUPSW I T H O U T FREE SUBSEMIGROUPSAbstract. The paper is inspired by the question of A. Shalev about possible coincidence of the class of collapsing groups and groups satisfying positive laws. We split theclass of collapsing groups for subclasses, corresponding to different functions on naturalnumbers and give a positive answer for some of them.1. IntroductionLet Ti be a free semigroup generated by x, y and let u(x, y), v(x, y) € Ti.By a (positive) law of degree n we mean here a binary expression(1)u(x,y) = v(x,y),where x (and y) has the same exponent sum on both sides; the first (andthe last) letters in u and v are different; the length of u (equal to the lengthof v) is n. From now on by a pair of elements we mean an ordered one. Wesay that a pair g, h of elements in a group satisfies a law (1) if the equalityu(g, h) = v(g, h) holds. A subset satisfies a law (1) if every pair of elementsin the subset does.Many authors considered properties of groups, which do not containnon-abelian free subsemigroups or, which is the same, groups with no

Journal

Demonstratio Mathematica – de Gruyter

Published: Jan 1, 2000

There are no references for this article.