Transitive Group

Author

Eric W. Weisstein
April 7, 2011

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GroupTheory/TransitiveGroup.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/TransitiveGroup.html.

©2011 Wolfram Research, Inc. except for portions noted otherwise

Examples

TransitiveGroupQ[#[]]&/@Symbol/@Names["MathieuGroupM*"]

{#,Transitivity[#[]]}&/@Symbol/@Names["MathieuGroupM*"]//Grid

Table[Transitivity[System`SymmetricGroup[n]],{n,10}]

Table[Transitivity[System`AlternatingGroup[n]],{n,10}]

{#,Transitivity[#[]]}&/@{ConwayGroupCo3,HigmanSimsGroupHS,SuzukiGroupSuz}//Grid

3-transitive

Date: 	Wed, 6 Apr 2011 08:34:56 -0500
From: 	Nick Wedd <nick@maproom.co.uk>

p1={{{a,b,c,d},{e,f,g,h}},{{a,f,c},{d,e,g}},{{e,f},{d,h},{b,c}}};

Transitivity@PermutationGroup[
Cycles/@p1/.Thread[(char=Union[Flatten[p1]])->Range[Length[char]]]]

p2={{{g,b,c,i,d},{j,e,h,f,l}},{{a,b,c},{d,e,f},{g,h,i},{j,k,l}},{{a,i},{d,g},{e,j},{h,k},{c,f}}};

Transitivity@PermutationGroup[
Cycles/@p2/.Thread[(char=Union[Flatten[p2]])->Range[Length[char]]]]