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Normal Subgroups of Groups Which Split Over The Infinite Cyclic Group
Author(s) -
Moon Myoungho
Publication year - 2000
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609399006578
Subject(s) - mathematics , normal subgroup , finitely generated abelian group , free product , combinatorics , group (periodic table) , cyclic group , mathematics subject classification , stallings theorem about ends of groups , locally finite group , finitely generated group , free group , product (mathematics) , pure mathematics , geometry , abelian group , chemistry , organic chemistry
Let G be either a free product with amalgamation A * C B 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.