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## Basic properties of blocks of a group action

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.1 Exercise 4.1.7 Let $G \leq S_A$ act transitively on the set $A$. A block is a nonempty subset…

## Stabilizer commutes with conjugation

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.1 Exercise 4.1.1 Let $G$ be a group and $A$ a nonempty set. Let $G$ act on $A$. Prove…

## The kernel and stabilizers of a group action are subgroups

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.7 Exercise 1.7.4 Let $G$ be a group acting on a set $A$. Show that the following sets are…

## Compute the stabilizer of an element under a given action of Sym(n)

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.15 Fix $i \in \{ 1, \ldots, n \} = A$, and let $S_n$ act on $A$…