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2000•Bulletin of the London Mathematical SocietyRequires access

Normal Subgroups of Groups Which Split Over The Infinite Cyclic Group

Myoungho Moon

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Abstract

Let G be either a free product with amalgamation A*CB or an HNN group A*C, where all normal subgroups of C are finitely generated. Suppose that both A and B have no non-trivial finitely generated normal subgroups of infinite indices. We show that if G contains a finitely generated normal subgroup N which intersects A or B non-trivially but is not contained in C, then the index of N in G is finite. 1991 Mathematics Subject Classification 20E06.

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Let G be either a free product with amalgamation A*CB or an HNN group A*C, where all normal subgroups of C are finitely generated. Suppose that both A and B have no non-trivial finitely generated normal subgroups of infinite indices. We show that if G contains a finitely generated normal subgroup N which intersects A or B non-trivially but is not contained in C, then the index of N in G is finite. 1991 Mathematics Subject Classification 20E06.

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Available abstract

Let G be either a free product with amalgamation A*CB or an HNN group A*C, where all normal subgroups of C are finitely generated. Suppose that both A and B have no non-trivial finitely generated normal subgroups of infinite indices. We show that if G contains a finitely generated normal subgroup N which intersects A or B non-trivially but is not contained in C, then the index of N in G is finite. 1991 Mathematics Subject Classification 20E06.

Key concepts: Mathematics, Normal subgroup, Finitely-generated abelian group, Free product, Combinatorics, Group (periodic table), Cyclic group, Mathematics Subject Classification

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