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On the profinite topology on solvable groups
 
 
Description:  We 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 the finitely generated free metabelian group is LERF, a result due to Coulbois.
We also show that the finitely generated free solvable group of degree three, which is not LERF, does not contain a strictly ascending {HNN}-extension of a finitely generated group. This settles, in the negative, a question of J. O. Button.
Date:  2018-05-23
Start Time:   15:30
Speaker:  Khadijeh Alibabaei (CMUP, Univ. Porto)
Institution:  CMUP, Univ. Porto
Place:  Room 5.5
Research Groups: -Algebra and Combinatorics
-Algebra, Logic and Topology
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