On the Surface Group Conjecture
نویسندگان
چکیده
We consider the following conjecture. Suppose that G is a non-free non-cyclic onerelator group such that each subgroup of finite index is again a one-relator group and each subgroup of infinite index is a free group. Must G be a surface group? We show that if G is a freely indecomposable fully residually free group and satisfies the property that every subgroup of infinite index is free then G is either a cyclically pinched one-relator group or a conjugacy pinched one-relator group. Further such a group G is either hyperbolic or free abelian of rank 2.
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