求描述上中心序列的有限p-群的幂零类的新算法
A new algorithm for finding the nilpotency class of a finite p-group describing the upper central series
摘要：
本文给出了求有界（或有限）阿贝尔p-群G的自同构群Aut（G）的极大正规p-子群N（G）的幂零类和上中心序列的一个算法。这是两篇论文的第一部分，致力于使用公式和算法计算N（G）的幂零类，这些算法几乎适用于所有群。在这里，我们证明了对于p>2，算法总是运行。该算法描述了Jacobson根J的一个理想序列，并且由于N（G）=J+1，该序列在N（G）中导出了上中心序列。
英文摘要：
In this paper we describe an algorithm for finding the nilpotency class, and the upper central series of the maximal normal p-subgroup N(G) of the automorphism group, Aut(G) of a bounded (or finite) abelian p-group G. This is the first part of two papers devoted to compute the nilpotency class of N(G) using formulas, and algorithms that work in almost all groups. Here, we prove that for p>2 the algorithm always runs. The algorithm describes a sequence of ideals of the Jacobson radical, J, and because N(G)=J+1, this sequence induces the upper central series in N(G).
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