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On the ranks of Fischer group \(\mathrm{Fi}_{23}\). (English) Zbl 1444.20008

Summary: Let \(G\) be a finite group and \(X\) be a conjugacy class of elements of \(G\). Then we define \(\operatorname{rank}(G:X)\) to be the minimum number of elements of \(X\) generating \(G\). In the present paper, we completely determined the \(\operatorname{rank}(\mathrm{Fi}_{23}:X)\) where \(X\) is a conjugacy classes of the Fischer’s second largest sporadic simple group \(\mathrm{Fi}_{23}\)

MSC:

20D08 Simple groups: sporadic groups
20F05 Generators, relations, and presentations of groups

Software:

GAP
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References:

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