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On Growth of Groups with Few Relators
Author(s) -
Wilson John S.
Publication year - 2004
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/s0024609303002674
Subject(s) - mathematics
Let G be a group that has a presentation with n generators and m relators, where m < n , and let S be an arbitrary generating set for G . Then some subset of n ‐ m elements of S freely generates a free subgroup of G . This leads to the proof of a conjecture of Gromov on growth of groups. 2000 Mathematics Subject Classification 20F05, 20E18.