Abstract

For a projectively invariant subgroup \(C\) of a reduced \(p\)-group \(G\), a nondecreasing sequence of ordinals and the symbol \(\infty\) is constructed in which the \(k\)th position, \(k=0,1,2,\dots\), is occupied by the minimum of heights in \(G\) of all nonzero elements of the subgroup \(p^kC[p]\). It is proved that if all elements of this sequence are integers, then the subgroup \(C\) is fully invariant.

中文翻译：

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阿贝尔$$p$$ -Groups 的投影不变子群

摘要

对于约减的\(p\) -群\(G\)的射影不变子群\(C\)，构造了一个非减序数序列和符号\(\infty\)，其中\(k\)第 th 个位置\(k=0,1,2,\dots\)被子群\(p^kC[p]\)的所有非零元素\(G\)中高度的最小值占据。证明如果该序列的所有元素都是整数，则子群\(C\)是完全不变的。