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OUTER AUTOMORPHISM GROUPS OF CERTAIN TREE PRODUCTS OF ABELIAN GROUPS

Part of: Low-dimensional topology Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  01 February 2008

Y. D. CHAI ,
YOUNGGI CHOI ,
GOANSU KIM  and
C. Y. TANG
Y. D. CHAI
Affiliation:
Sungkyunkwan University, Suwon, 440-746, Korea (email: ydchai@yurim.skku.ac.kr)
YOUNGGI CHOI
Affiliation:
Seoul National University, Seoul, 151-742, Korea (email: yochoi@snu.ac.kr)
GOANSU KIM
Affiliation:
Yeungnam University, Kyongsan, 712-749, Korea (email: gskim@ynucc.yeungnam.ac.kr)
C. Y. TANG
Affiliation:
University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada (email: fcytang@math.uwaterloo.ca)
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Abstract

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We prove that certain tree products of finitely generated Abelian groups have Property E. Using this fact, we show that the outer automorphism groups of those tree products of Abelian groups and Brauner’s groups are residually finite.

Keywords

outer automorphism groupsgeneralized free productsresidually finiteconjugacy separable

MSC classification

Secondary: 20E26: Residual properties and generalizations; residually finite groups 20E06: Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 57M05: Fundamental group, presentations, free differential calculus
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 1 , February 2008 , pp. 9 - 20
Copyright
Copyright © Australian Mathematical Society 2008

References

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