The probability of generating a finite simple group
The probability of generating a finite simple group
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DOI：
10.1007/s11856-013-0034-7
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发表时间：
2013-07
影响因子：
1
通讯作者：
Nina E. Menezes;M. Quick;C. Roney-Dougal
中科院分区：
文献类型：
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作者：
Nina E. Menezes;M. Quick;C. Roney-Dougal
本文研究了有限单群的生成概率及其推广PG，socG（d），由元素生成几乎单群G的条件概率，给定这些元素生成G/socG.本文证明了PG，socG（2）≠ 53/90，等式成立当且仅当G是A6或S6，并对PG，socG（3）建立了类似的结果.积极的答案长期存在的问题Wiegold的直接产品，和梅尔'nikov profinite群，很容易从我们的结果。
We study the probability of generating a finite simple group, together with its generalisationPG,socG(d), the conditional probability of generating an almost simple finite groupGbydelements, given that these elements generateG/socG. We prove thatPG,socG(2) ⩽ 53/90, with equality if and only ifGis A6or S6, and establish a similar result forPG,socG(3). Positive answers to longstanding questions of Wiegold on direct products, and of Mel’nikov on profinite groups, follow easily from our results.