Premium
Finiteness properties and profinite completions
Author(s) -
Lubotzky Alexander
Publication year - 2014
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdt070
Subject(s) - mathematics , profinite group , finitely generated abelian group , type (biology) , pure mathematics , discrete mathematics , group (periodic table) , ecology , chemistry , organic chemistry , biology
In this note, we show that various (geometric/homological) finiteness properties are not profinite properties. For example, for all positive integers k and ℓ, there exist two finitely generated residually finite groups Γ 1 and Γ 2 with isomorphic profinite completions, such that Γ 1 is strictly of type F k and Γ 2 of type F ℓ .
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom