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## Use Sylow’s Theorem to prove Cauchy’s Theorem

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.5 Exercise 4.5.1 Solution: Let $G$ be a finite group and $p$ a prime dividing $|G|$. By Sylow’s Theorem,…

## Permissible subgroup orders in a group of order 120, and their indices

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.1 Which of the following are permissible orders for subgroups of a group of order 120: 1,…