一类中心循环的有限p -群的自同构群的研究

摘要

本文研究了一类中心循环的有限p -群G 的自同构群。利用在G 的导群上作用平凡的自同构以及环上的辛群和正交群，确定了G的自同构群的结构，这推广了Bornand的相应结果。%In this article, the automorphism group of a class of a finite p-group G with a cyclic center is researched. With the automorphisms which act trivially on the derived subgroup of G, symplectic group and orthogonal group over a ring, the structure of the automorphism group of G is determined, which generalizes the related results of Bornand.