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INDICABLE GROUPS AND ENDOMORPHIC PRESENTATIONS
Published online by Cambridge University Press: 12 December 2011
Abstract
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In this paper 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 ⋊ ℤ, where H has finite ascending endomorphic presentation.
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- Copyright © Glasgow Mathematical Journal Trust 2011
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