Prime Power Graphs for Groups of Lie Type
Prime Power Graphs for Groups of Lie Type
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李型群的素幂图
DOI：
10.1006/jabr.2001.9016
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
Á. Seress
中科院分区：
文献类型：
--
作者：
W. Kantor;Á. Seress
我们给每个有限的李型单群G配一个权图Δ（G）。我们证明了，在一个明确的例外列表中，Δ（G）决定G直到同构，并且对于这些例外，Δ（G）仍然决定G的特征。这一结果是由算法的考虑。证明了对任意有限的Lie型单群G，输入为一个黑箱群，并有一个预言机来计算群元素的阶，Δ（G）和G的特征线都可以在输入长度上用时间多项式用Monte Carlo算法计算.在以往的构造性识别算法中，需要将该特征作为输入的一部分。
Abstract We associate a weighted graph Δ( G ) to each finite simple group G of Lie type. We show that, with an explicit list of exceptions, Δ( G ) determines G up to isomorphism, and for these exceptions, Δ( G ) nevertheless determines the characteristic of G . This result was motivated by algorithmic considerations. We prove that for any finite simple group G of Lie type, input as a black-box group with an oracle to compute the orders of group elements, Δ( G ) and the characteristic of G can be computed by a Monte Carlo algorithm in time polynomial in the input length. The characteristic is needed as part of the input in a previous constructive recognition algorithm for G .
DOI：
10.1090/s0002-9947-1987-0896007-9
发表时间：
1987
影响因子：
1.3
作者：
D. Deriziotis;G. Michler
通讯作者：
D. Deriziotis;G. Michler