Let G be a group and \(\mathrm{IA}(G)\) denote the group of all automorphisms of G, which induce identity map on the abelianized group \(G_{ab}=G/G'\). Also the group of those \(\mathrm{IA}\)-automorphisms which fix the centre element-wise is denoted by \(\mathrm{IA_Z}(G)\). In the present article, among other results and under some condition we prove that the derived subgroups of finite p-groups, for which \(\mathrm{IA_Z}\)-automorphisms are the same as central automorphisms, are either cyclic or elementary abelian.

中文翻译：

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$$ \ mathrm {IA_Z} $$ IA Z上的某些属性-组的自同构

让G ^是一个群，\（\ mathrm {IA}（G）\）表示的基团的所有构的ģ，从而诱发身份地图上的abelianized组\（G_ {AB} = G / G'\） 。那些固定中心元素的\（\ mathrm {IA} \）-自同构的组也用\（\ mathrm {IA_Z}（G）\）表示。在本文章中，除其它结果和一些条件下，我们证明了有限的衍生亚群p -基团，对此\（\ mathrm {IA_Z} \） -automorphisms是相同的中央构，或者是环状的或基本阿贝尔。