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Primes and automorphisms

Source: Romanian District Olympiad 2016, Grade XII, Problem 3

October 5, 2018
modular arithmeticgroup theorysuperior algebra

Problem Statement

Let be a group G G of order 1+p, 1+p, where p p is and odd prime. Show that if p p divides the number of automorphisms of G, G, then p≡3(mod4). p\equiv 3\pmod 4.
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