Conjugacy separability and outer automorphism groups of certain HNN extensions
Conjugacy separability and outer automorphism groups of certain HNN extensions
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DOI：
10.1016/j.jalgebra.2011.02.038
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发表时间：
2011-05
影响因子：
0.9
通讯作者：
K. B. Wong;P. Wong
中科院分区：
文献类型：
--
作者：
K. B. Wong;P. Wong
本文首先建立了具有中心关联子群的有限多环群的HNN扩展的共轭可分性判据。利用这一结果，证明了这些HNN扩展的剩余有限性和共轭可分性的等价性。然后证明了如果HNN扩展本身是残有限的，则这些HNN扩展的外自同构群是残有限的。
In this note we first establish a criterion for the conjugacy separability of HNN extensions of polycyclic-by-finite groups with central associated subgroups. Using this result, we prove the equivalence of residually finiteness and conjugacy separability in these HNN extensions. Then we prove that the outer automorphism groups of these HNN extensions are residually finite if the HNN extensions themselves are residually finite.