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Re: Recognizing finite groups in Mathematica 7



jamievicary at NgOmSaPiAlM.com wrote:

> Hi all. Mathematica 7 has great finite group functionality, which

> includes knowledge of the common names of many group. I have an

> algorithm that produces multiplication tables for different groups ---

> how can I get Mathematica to recognize which group has been produced,

> and name it for me?

> 

> Thanks,

> Jamie.

> 

Hi Jamie,

FiniteGroupData[] gives the names of all groups known to Mathematica. We may now 

select the one that has the given multiplication table.

Assume that mt contains the multiplication table, e.g.:

mt = {{1, 2, 3, 4, 5, 6, 7, 8}, {2, 5, 4, 7, 6, 1, 8, 3}, {3, 8, 5, 2,

      7, 4, 1, 6}, {4, 3, 6, 5, 8, 7, 2, 1}, {5, 6, 7, 8, 1, 2, 3,

     4}, {6, 1, 8, 3, 2, 5, 4, 7}, {7, 4, 1, 6, 3, 8, 5, 2}, {8, 7, 2,

     1, 4, 3, 6, 5}};

the the following gives the name:

Select[FiniteGroupData[],

  FiniteGroupData[#, "MultiplicationTable"] === mt &]

Daniel






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