More on this later

[annie_lyne]

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

Comments

[puellavulnerata]

Hmm. I'm feeling a bit more brainful than yesterday, so I tried reading this again.

Now, it seems to me that the Pα and the σi are both matrices of real numbers, so how is the Cayley table, with its entries being group elements, the sum of products of those?