Let G be finite with |G| > 1. If Aut(G) acts transitively on G ?...

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Let G be finite with |G| > 1. If Aut(G) acts transitively on G ? {e} then G ?= (Z/(p))n for some prime p.

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Proof Elements that are linked by an automorphism have the same order so the hypothesis in the theorem implies all nonidentity elements of G have the same order Let p be a prime factor of G Cauchys theorem gives us an element with order p so all nonidentity elements have order p See Answer

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Let G be finite with |G| > 1. If Aut(G) acts transitively on G ?...

60.1K

Verified Solution

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Advance Math

Let G be finite with |G| > 1. If Aut(G) acts transitively on G ? {e} then G ?= (Z/(p))n for some prime p.

Answer & Explanation Solved by verified expert

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