On the profinite topology on solvable groups
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AbstractWe show that the wreath product of a finitely generated abelian group with a polycyclic group is a LERF group. This theorem yields as a corollary that finitely generated free metabelian groups are LERF, a result due to Coulbois. We also show that a free solvable group of class 3 and rank at least 2 does not contain a strictly ascending HNN-extension of a finitely generated group. Since such groups are known not to be LERF, this settles, in the negative, a question of J. O. Button.
2015 ◽
Vol 25
(05)
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pp. 917-926
2012 ◽
Vol 22
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pp. 1250012
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2010 ◽
Vol 17
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pp. 799-802
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1975 ◽
Vol 78
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pp. 357-368
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2006 ◽
Vol 16
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pp. 875-886
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2018 ◽
Vol 28
(08)
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pp. 1613-1632
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1971 ◽
Vol 12
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pp. 145-160
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