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On finitely presented soluble groups with small abelian‐by‐finite images
Author(s) -
Wilson John S.
Publication year - 2013
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdt007
Subject(s) - abelian group , citation , subject (documents) , computer science , library science , mathematics , information retrieval , world wide web , combinatorics
The main result of [7] asserted that if G is a finitely presented soluble group and no subgroup of finite index maps epimorphically to Z then G is virtually nilpotent-by-cyclic. One important ingredient in the proof was Theorem A of Brookes [2]. We have recently become aware that Brookes’ result requires stronger hypotheses than those stated in [2]. As a consequence, the proof of the above assertion is lacunary, and indeed counter-examples have been found by Victor Bludov. Let p be a prime and let G be the group with presentation