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## Consequences of equality among left and right cosets

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.6 Let $G$ be a group, $H \leq G$ a subgroup, and $g \in G$ a fixed…

## The centralizer and normalizer of a group center is the group itself

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.2 Exercise 2.2.2 Let $G$ be a group. Prove that $C_G(Z(G)) = G$ and deduce that $N_G(Z(G)) = G$.…