Editing Alternating group (section)

==Examples S<sub>4</sub> and A<sub>4</sub>==
{|
|-
|  style="vertical-align:top;"|[[File:Symmetric group 4; Cayley table; numbers.svg|thumb|350px|[[Cayley table]] of the [[symmetric group]] S<sub>4</sub><br><br>The [[Parity of a permutation|odd permutations]] are colored:<br>[[Transposition (mathematics)|Transpositions]] in green and [[Cycles and fixed points|4-cycles]] in orange]] || &nbsp;&nbsp;&nbsp; ||  style="vertical-align:top;"|[[File:Alternating group 4; Cayley table; numbers.svg|thumb|350px|Cayley table of the alternating group A<sub>4</sub><br>Elements: The even permutations (the identity, eight [[Cycles and fixed points|3-cycles]] and three <nowiki>double-</nowiki>[[Transposition (mathematics)|transpositions]] (double transpositions in boldface))<br><br>Subgroups:<br>[[File:Klein four-group; Cayley table; subgroup of S4 (elements 0,7,16,23).svg|70px|Klein four-group]]<br>[[File:Cyclic group 3; Cayley table; subgroup of S4 (elements 0,3,4).svg|60px|Cyclic group Z3]]  [[File:Cyclic group 3; Cayley table; subgroup of S4 (elements 0,8,12).svg|60px|Cyclic group Z3]]  [[File:Cyclic group 3; Cayley table; subgroup of S4 (elements 0,11,19).svg|60px|Cyclic group Z3]]  [[File:Cyclic group 3; Cayley table; subgroup of S4 (elements 0,15,20).svg|60px|Cyclic group Z3]]]]
|}

{| class=wikitable
|+ [[Cycle graph (algebra)|Cycle graphs]]
|- align=center valign=top 
| [[File:GroupDiagramMiniC3.svg|200px]]<BR>A<sub>3</sub> = Z<sub>3</sub> (order 3)
| [[File:GroupDiagramMiniA4.svg|200px]]<BR>A<sub>4</sub> (order 12)
| [[File:GroupDiagramMiniA4xC2.png|200px]]<BR>A<sub>4</sub> × Z<sub>2</sub> (order 24)
|- align=center valign=top 
|[[File:GroupDiagramMiniD6.svg|200px]]<BR>S<sub>3</sub> = Dih<sub>3</sub> (order 6)
|[[File:Symmetric group 4; cycle graph.svg|200px]]<BR>S<sub>4</sub> (order 24)
|[[File:Alternating group 4; cycle graph; subgroup of S4.svg|200px]]<BR>A<sub>4</sub> in S<sub>4</sub> on the left
|}