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- W2022983220 abstract "A group G is knot-like if it is finitely presented of deficiency 1 and has abelianization G / G ′ ≃ Z . We prove the conjecture of E. Rapaport Strasser that if a knot-like group G has a finitely generated commutator subgroup G ′ then G ′ should be free in the special case when the commutator G ′ is residually finite. It is a corollary of a much more general result : if G is a discrete group of geometric dimension n with a finite K ( G , 1 ) -complex Y of dimension n , Y has Euler characteristics 0, N is a normal residually finite subgroup of G , N is of homological type FP n - 1 and G / N ≃ Z then N is of homological type FP n and hence G / N has finite virtual cohomological dimension vcd ( G / N ) = cd ( G ) - cd ( N ) . In particular either N has finite index in G or cd ( N ) ⩽ cd ( G ) - 1 . Furthermore we show a pro- p version of the above result with the weaker assumption that G / N is a pro- p group of finite rank. Consequently a pro- p version of Rapaport's conjecture holds." @default.
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- W2022983220 date "2006-03-01" @default.
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- W2022983220 title "On a conjecture of E. Rapaport Strasser about knot-like groups and its pro-p version" @default.
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- W2022983220 doi "https://doi.org/10.1016/j.jpaa.2005.06.008" @default.
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