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Right Orderable Residually Finite p-Groups and a Kourovka Notebook Problem

✍ Scribed by Peter A. Linnell


Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
50 KB
Volume
248
Category
Article
ISSN
0021-8693

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✦ Synopsis


Rhemtulla proved that if a group is a residually finite p-group for infinitely many primes p, then it is two-sided orderable. In problem 10.30 of The Kourovka Notebook (14th ed.), N. Ya. Medvedev asked if there is a non-right-orderable group which is a residually finite p-group for at least two different primes p. Using a result of Witte, we will show that many subgroups of finite index in GL give examples of such groups. On the other hand, we will show that no such example can exist among solvable by finite groups.  2002 Elsevier Science (USA)