When is a right orderable group

locally indicable?

Authors:
Patrizia Longobardi, Mercede Maj and Akbar Rhemtulla

Journal:
Proc. Amer. Math. Soc. **128** (2000), 637-641

MSC (1991):
Primary 20F19; Secondary 06F15, 20F60

DOI:
https://doi.org/10.1090/S0002-9939-99-05534-3

Published electronically:
October 25, 1999

MathSciNet review:
1694872

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If a group has an ascending series of subgroups such that for each ordinal , and has no non-abelian free subsemigroup, then is right orderable if and only if it is locally indicable. In particular if is a *radical-by-periodic* group, then it is right orderable if and only if it is locally indicable.

**[1]**G.M.Bergman,*Right-orderable groups that are not locally indicable*, Pac. J. Math.**147**(1991), 243-248. MR**92e:20030****[2]**R.G.Burns and V.W.Hale,*A note on group rings of certain torsion-free groups*, Can. Math. Bull.**15**(1972), 441-445. MR**46:9149****[3]**I.M.Chiswell and P.H.Kropholler,*Soluble right orderable groups are locally indicable*, Can. Math. Bull.**36**(1993), 22-29. MR**93j:20088****[4]**P.M. Cohn,*Groups of order automorphisms of ordered sets*, Mathematika**4**(1957), 41-50. MR**19:940e****[5]**P.F. Conrad,*Right-ordered groups*, Mich. Math. J.**6**(1959), 267-275. MR**21:5684****[6]**V.M. Kopitov and N. Ya. Medvedev,*Right Ordered Groups*, Siberian School of Algebra and Logic, Plenum Publishing Corporation, New York, 1996.**[7]**P. Longobardi, M. Maj and A. H. Rhemtulla,*Groups with no free subsemigroups*, Trans. Amer. Math. Soc.**347**(1995), 1419-1427. MR**95g:20043****[8]**A. Yu. Ol'shanski and A. Storozhev,*A group variety defined by a semigroup law*, J. Austral. Math. Soc. (Series A)**60**(1996), 255-259. MR**97b:20033****[9]**A. H. Rhemtulla,*Polycyclic right ordered groups*, Algebra, Carbondale 1980, Lecture Notes in Mathematics 848 (R.K.Amayo, ed.), Springer Berlin, 1981, pp. 230-234. MR**82i:06025****[10]**V.M. Tararin,*On Radically right-ordered groups*, Sib. Mat. Zh.**32**(1991), 203-204.**[11]**M.I. Zaitseva,*Right-ordered groups*, Uchen. Zap. Shuisk. Gos. Ped. Inst.**6**(1958), 215-226.

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Additional Information

**Patrizia Longobardi**

Affiliation:
Dipartimento di Matematica e Applicazioni “R. Caccioppoli", via Cintia, Monte S. Angelo, 80126, Napoli, Italy

Email:
longobar@matna2.dma.unina.it

**Mercede Maj**

Affiliation:
Dipartimento di Matematica e Informatica, via Salvator Allende, 84081 Baronissi (Salerno), Italy

Email:
maj@matna2.dma.unina.it

**Akbar Rhemtulla**

Affiliation:
Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

Email:
akbar@malindi.math.ualberta.ca

DOI:
https://doi.org/10.1090/S0002-9939-99-05534-3

Received by editor(s):
March 15, 1998

Published electronically:
October 25, 1999

Additional Notes:
The third author wishes to thank NSERC for partial financial support.

Communicated by:
Ronald M. Solomon

Article copyright:
© Copyright 1999
American Mathematical Society