Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2012; 49(5): 949-959

Printed September 30, 2012

https://doi.org/10.4134/BKMS.2012.49.5.949

Copyright © The Korean Mathematical Society.

Class-preserving automorphisms of generalized free products amalgamating a cyclic normal subgroup

Wei Zhou and Goansu Kim

Southwest University, Yeungnam University

Abstract

In general, a class-preserving automorphism of generalized free products of nilpotent groups, amalgamating a cyclic normal subgroup of order 8, need not be an inner automorphism. We prove that every class-preserving automorphism of generalized free products of finitely generated nilpotent groups, amalgamating a cyclic normal subgroup of order less than $8$, is inner.

Keywords: class-preserving automorphisms, generalized free products, nilpotent groups, residually finite

MSC numbers: Primary 20E26, 20E06, 20F34