CH 9 - Sylow's Theorem

Question 1

Define a p-subgroup.

Define a Sylow p-subgroup of G.

Answer 1

Question 2

State Sylow’s Theorem.

Answer 2

Question 3

State a lemma onn p, Q, G & R.

State and prove a lemma on the size of the G-orbit, Sigma.

Answer 3

Question 4

State a result on groups with a unique Sylow p-subgroup, P.

Are there simple groups of order 40, 70, 56?

Answer 4

Question 5

For each prime p dividing 60, determine the number of Sylow p-subgroups of
the alternating group A5.

Answer 5