Let G = { σ1, ..., σn} be a finite group with the σi the regular representation of G. Denote C(G) as the Cayley table of G (as a matrix) and Pα the permutation matrix of the permutation α.
Then C(G) = σ1 Pτ1 + ... + σn Pτn for some { τ1, ..., τn } ∈ Sn. Define φ(σi) = τi in this way.
Let f : G → G ; f( x ) = x− 1. This function is obviously
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