Class-preserving automorphisms and inner automorphisms of certain tree products of groups
Class-preserving automorphisms and inner automorphisms of certain tree products of groups
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DOI：
10.1016/j.jalgebra.2011.05.036
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发表时间：
2011-09
影响因子：
0.9
通讯作者：
Wei Zhou-;Goansu Kim
中科院分区：
文献类型：
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作者：
Wei Zhou-;Goansu Kim
一般来说，幂零群的广义自由积的类保持自同构不一定是内自同构。我们证明，合并无限循环子群的有限生成的幂零群或自由群的树积的每一个保类自同构都是内部的。由此可见，合并无限循环子群的此类树积的外自同构群是残差有限的。
In general, a class-preserving automorphism of generalized free products of nilpotent groups need not be an inner automorphism. We prove that every class-preserving automorphism of tree products of finitely generated nilpotent or free groups, amalgamating infinite cyclic subgroups, is inner. It follows that the outer automorphism groups of such tree products, amalgamating infinite cyclic subgroups, are residually finite.