Cayleys_theorem

introduction

%%visits: 5 ## intuition ## rigour ## exam clinic ## examples and non-examples ## resources tags :math:

Cayley’s theorem

We can permute the elemenst of G, by g : g_i → g_j by gg_i = g_j and so each group element in G may be associated with a permutation i.e. if gg_i = g^′_i then $g = \begin{pmatrix} g_1&g_2&g_3& \ldots &g_{|g|} \\ g_1&g_2&g_3& \ldots &g_{|g|} \end{pmatrix}$ is a permutation within S_|g|. So it defines a permutation so it must be a subset etc. :todo:

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