## Prove that the augmentation ideal of a given group ring is nilpotent

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.29 Solution: We begin with some lemmas. Lemma 1: Let $\pi : G \rightarrow H$ be a…

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.2 Exercise 4.2.9 Solution: Let $G$ be a group of order $p^k$ and $H \leq G$ a subgroup with…