algebra / Combinatorial Group Theory
Baumslag asked whether a one-relator group $G=F/\langle\langle r\rangle\rangle$ with $r$ a commutator is Hopfian, residually finite or automatic. The paper constructs a family $G_m=\langle a,t \mid [t,a[a,t]^{-m}]\rangle$ answering all three negatively.
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Append-only history
Baumslag asked whether a one-relator group $G=F/\langle\langle r\rangle\rangle$ with $r$ a commutator is Hopfian, residually finite or automatic. The paper constructs a family $G_m=\langle a,t \mid [t,a[a,t]^{-m}]\rangle$ answering all three negatively.
Research memory
Baumslag asked whether a one-relator group $G=F/\langle\langle r\rangle\rangle$ with $r$ a commutator is Hopfian, residually finite or automatic. The paper constructs a family $G_m=\langle a,t \mid [t,a[a,t]^{-m}]\rangle$ answering all three negatively.
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