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Right orderable residually finite p-groups and a Kourovka notebook problem | | Peter A. Linnell
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12 Jul 2001 | | Subject: | Group Theory MSC-class: 20F20 (Primary) 06F15 (Secondary) | math.GR | | Abstract: | A. H. 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. edition, 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 Dave Witte, we will show that many subgroups of finite index in GL_3(Z) give examples of such groups. On the other hand we will show that no such example can exist among solvable by finite groups. | | Source: | arXiv, math.GR/0107094 | | Services: | Forum | Review | PDF | Favorites | |
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