Black box exceptional groups of Lie type

Black box exceptional groups of Lie type
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黑盒李型异常群

DOI：
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发表时间：
2011
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通讯作者：
Kay Magaard
Kay Magaard
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文献类型：
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作者：
W. Kantor;Kay Magaard

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如果已知黑箱群同构于已知大小的域上任何F4(Q)以外的(扭曲的)秩为&gt；1的李型例外单群，给出一个生成构造性同构的拉斯维加斯算法。考虑到它的时序，当输入群没有与任何群F4(Q)或G2(Q)同构的合成因子时，该算法将所有已知的近线性时间蒙特卡罗置换群算法升级为拉斯维加斯算法。
If a black box group is known to be isomorphic to an exceptional simple group of Lie type of (twisted) rank > 1, other than any F4(q), over a field of known size, a Las Vegas algorithm is given to produce a constructive isomorphism. In view of its timing, this algorithm yields an upgrade of all known nearly linear time Monte Carlo permutation group algorithms to Las Vegas algorithms when the input group has no composition factor isomorphic to any group F4(q) or G2(q).