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## Compute some orbits of an action by Sym(4) on polynomials in four variables

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.1 Exercise 4.1.6 As in Exercise 2.2.12, let $S_4$ act on the set $R$ of all polynomials with integer…

## Transitive group actions induce transitive actions on the orbits of the action of a subgroup

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.1 Exercise 4.1.9 Suppose $G \leq S_A$ acts transitively on $A$ and let $H \leq G$ be normal. Let…