$S_4$ — Adjacent Transpositions
Minimal local moves generate the whole group.
Visualization of Algebraic Structures — Symmetric Groups
Interactive Cayley graphs with scholarly, readable presentation.
About this Project
This website presents interactive visualizations of Cayley graphs for the symmetric group $S_n$, emphasizing how different generating sets and subgroup structures shape the geometry of the graph. Explanations and notation are typeset with MathJax for clarity.
Quick Access
$S_4$ — Transposition & 4-cycle
A contrasting generating pair and resulting geometry.
$S_4$ — via $A_4$
Structure induced by the alternating subgroup.
$S_4$ — via $C_4$
Cyclic subgroup perspective and adjacency geometry.
$S_4$ — via $D_4$
Graph induced by the dihedral subgroup.
Graph Viewer
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Select a graph from Quick Access or the left menu to display it here.