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ICMC 2019/20 Round 2, Problem 1

Source: Imperial College Mathematics Competition 2019/20 - Round 2

August 7, 2020
college contestsgroup theory

Problem Statement

An [I]automorphism of a group (G,∗)\left(G,*\right) is a bijective function f:G→Gf:G\to G satisfying f(x∗y)=f(x)∗f(y)f(x*y)=f(x)*f(y) for all x,y∈Gx,y\in G. Find a group (G,∗)(G,*) with fewer than (201.6)2=40642.56(201.6)^2=40642.56 unique elements and exactly 201622016^2 unique automorphisms.
Proposed by the ICMC Problem Committee
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