Abstract Algebra: Theory and Applications · Problem 14.5.5

The Sylow Theorems — Thomas Judson

Mathematics — Abstract Algebra · conjugation-action-a4

Problem

Let

G = A_4

and suppose that

G

acts on itself by conjugation; that is,

(g, h) \mapsto ghg^{-1}

. (a) Determine the conjugacy classes (orbits) of each element of

G

. (b) Determine all of the isotropy subgroups for each element of

G