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cute from IMC

Source: IMC 1997/problem B5

June 13, 2004
algebra proposedalgebra

Problem Statement

Let XX be an arbitrary set and ff a bijection from XX to XX. Show that there exist bijections g, g′:X→Xg,\ g':X\to X s.t. f=g∘g′, g∘g=g′∘g′=1Xf=g\circ g',\ g\circ g=g'\circ g'=1_X.
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