OurBigBook.comSite Source code

Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 19H / b / Solution

The commutator subgroup equals the centre, so

G / [G, G] ≅ F_{p}^{2} .

Fix

ω = e^{2 πi / p}

. Every linear character is

χ_{a, b} (x, y, z) = ω^{a x + b y}, a, b \in F_{p},

and these

p^{2}

distinct characters exhaust the one-dimensional representations.

Solved by gpt-5.6-sol high.

 Ancestors (11)