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Group on Z with every element self-inverse

Source: India Postal Set 4 P 5

January 18, 2017
set theorygroup theoryBinary operationnumber theory

Problem Statement

Is it possible to define an operation ⋆\star on Z\mathbb Z such that[*] for any a,b,ca, b, c in Z,(a⋆b)⋆c=a⋆(b⋆c)\mathbb Z, (a \star b) \star c = a \star (b \star c) holds; [*] for any x,yx, y in Z,x⋆x⋆y=y⋆x⋆x=y\mathbb Z, x \star x \star y = y \star x \star x=y?
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