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Standard generators for \(J_ 3\). (English) Zbl 0852.20027
Given two representations (by permutations or matrices) of a sporadic simple group it may be difficult to explicitly construct an isomorphism by giving images in the second representation of generators in the first representation. Are there pairs of generators \((g_1,g_2)\) of the represented abstract group which are computationally easy to find in a concrete representation and characterized up to (inner) automorphisms by computationally accessible properties? When such standard generators are agreed upon, representatives for conjugacy classes and generators for maximal subgroups may be published as words in these standard generators and then easily computed in a concrete representation of the group. The authors explain how this can be done for the groups \(J_3\) and \(J_3 : 2\) in a consistent way and refer to recent work of the second author [J. Algebra 184, 505-515 (1996)] with respect to the other sporadic simple groups.

MSC:
20F05 Generators, relations, and presentations of groups
20-04 Software, source code, etc. for problems pertaining to group theory
20D08 Simple groups: sporadic groups
Software:
Cayley; GAP
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References:
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