Bulletin of the London Mathematical Society

Table of Contents - 2000 - Volume 32, Issue 01  


NOTES AND PAPERS

NORMAL SUBGROUPS OF GROUPS WHICH SPLIT OVER THE INFINITE CYCLIC GROUP

MYOUNGHO MOON a1
a1 Department of Mathematics Education, Konkuk University, Seoul 143-701, Korea

Abstract

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.

(Received September 9 1997)
(Revised January 22 1998)
(Revised September 24 1998)