Explore BrainMass

Sylow's Theorem Problems

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

Verify that if H is a subgroup of G, and a ? G, then aHa^-1 is a subgroup of G.

Prove that if H is a finite subgroup of G, and a ? G, then |aHa^-1| = |H|. (Suggestion: The mapping h ? aha^-1 is one-to-one.)

Explain why if H is a Sylow p-subgroup of a finite group, then so is each conjugate of H.

Prove that if a finite group has only one Sylow p-subgroup for some prime p, then that subgroup must be normal.

© BrainMass Inc. brainmass.com October 16, 2018, 1:22 pm ad1c9bdddf - https://brainmass.com/math/algebra/sylow-theorem-problems-519325

Solution Summary

This solution explains how to solve problems related to Sylow's theorem.