Abstract Algebra: Theory and Applications · Problem 15.4.1

Rings — Thomas Judson

Mathematics — Abstract Algebra · sylow-theorems

Problem

What are the orders of all Sylow

p

-subgroups where

G

has order 18, 24, 54, 72, and 80? Hint. If

|G| = 18 = 2 \cdot 3^2

, then the order of a Sylow 2-subgroup is 2, and the order of a Sylow 3-subgroup is 9.