Proving Nonabelian Simple Group Can't Operate on Fewer than 5 Elements

Thread starter Dragonfall
Start date Nov 9, 2006
Tags

Group

Join the discussion

Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.

Real named experts · corrections over time · the nuance an AI answer skips

1 reply · 2K views

Dragonfall

Thread starter
Nov 9, 2006

How can I prove the following:

A nonabelian simple group can not operate nontrivially on a set containing fewer than five elements.

I can't get started.

Physics news on Phys.org

Materials surrounding a fusion reaction can dramatically increase how often it occurs
Chocolate syrup-like fluid stores multiple interacting memories
Engineers observe quantum heat waves at room temperature

StatusX

Homework Helper

Nov 9, 2006

When a group acts on a set of n elements, you get a homomorphism from that group into S_n. What can the kernel of this homomorphism be?

Proving Nonabelian Simple Group Can't Operate on Fewer than 5 Elements

Hi! Can someone explain about Differential Equations?

Deriving spatial derivatives

Investigating the real roots of a cubic equation

What does "compute Aut(G)" mean?

J_1(x) = (x^2/10)*(J_1(x) + J_3(x)) How to solve?

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Proving Nonabelian Simple Group Can't Operate on Fewer than 5 Elements

Similar threads