Re: Recognizing finite groups in Mathematica 7

*To*: mathgroup at smc.vnet.net*Subject*: [mg102567] Re: Recognizing finite groups in Mathematica 7*From*: dh <dh at metrohm.com>*Date*: Fri, 14 Aug 2009 05:59:36 -0400 (EDT)*References*: <h46p4m$e5l$1@smc.vnet.net>

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

**Follow-Ups**:**Re: Re: Recognizing finite groups in Mathematica 7***From:*Ron Monson <ron.monson@yahoo.com>