  In this note we look at presentations of subgroups of finitely presented
groups with infinite cyclic quotients. We prove that if $H$ is a finitely
generated normal subgroup of a finitely presented group $G$ with $G/H$ cyclic,
then $H$ has ascending finite endomorphic presentation. It follows that any
finitely presented indicable group without free semigroups has the structure of
a semidirect product $H \rtimes \field{Z}$ where $H$ has finite ascending
endomorphic presentation.

Group Theory