Group Action27

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 Exer...
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 \le...
Every doubly transitive group action is primitive
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.1 Exercise 4.1.8 A transiti...
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...
Compute the orbits, cycle decompositions, and stabilizers of some given group actions of Sym(3)
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.1 Exercise 4.1.4 Let $S_3$ ...
An abelian group has the same cardinality as any sets on which it acts transitively
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.1 Exercise 4.1.3 Suppose $G...
Stabilizer commutes with conjugation
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.1 Exercise 4.1.1 Solution: ...
Characterization of the orbits of a group action as equivalence classes
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.7 Exercise 1.7.18 Let $H$ b...
Conjugation by a fixed group element is an automorphism
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.7 Exercise 1.7.17 Let $G$ b...
Conjugation is a group action
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.7 Exercise 1.7.16 Let $G$ b...