Even Permutations as a Product of Two Conjugate Cycles
Even Permutations as a Product of Two Conjugate Cycles
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偶数排列作为两个共轭循环的乘积
DOI：
10.1016/0097-3165(72)90102-1
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发表时间：
1972
期刊：
影响因子：
--
通讯作者：
E. Bertram
中科院分区：
文献类型：
--
作者：
E. Bertram
本文的中心结果是定理的推广：对于n≥ 5，定义在n个符号上的每个偶置换是偶置换a和B的交换子a B a− 1 B− 1。特别地，[3 n 4]<$l <$n被证明是关于l的充要条件，以便定义在n <$5个符号上的每个偶置换可以表示为两个周期的乘积，每个周期的长度为l。各种结果如下，包括那些l的特征，其中每一个奇置换是一个长度为l的循环和一个长度为l+ 1的循环的产品。
The central result of this paper is a generalization of the theorem that, for n≥ 5, every even permutation defined on n symbols is a commutator a b a− 1 b− 1 of even permutations a and b. In particular,[3n 4]⩽ l⩽ n is shown to be the necessary and sufficient condition on l, in order that every even permutation defined on n⩾ 5 symbols can be expressed as a product of two cycles, each of length l. Various results follow, including the characterization of those l for which every odd permutation is a product of a cycle of length l and a cycle of length l+ 1.