Class-preserving automorphisms of generalized free products amalgamating a cyclic normal subgroup
Bull. Korean Math. Soc. 2012 Vol. 49, No. 5, 949-959
https://doi.org/10.4134/BKMS.2012.49.5.949
Printed September 30, 2012
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
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