Abstract Algebra: Theory and Applications · Problem 14.5.1

The Sylow Theorems — Thomas Judson

Mathematics — Abstract Algebra · group-actions-equivalence-classes

Problem

Examples 14.1.1--14.1.5 in the first section each describe an action of a group

G

on a set

X

, which will give rise to the equivalence relation defined by

G

-equivalence. For each example, compute the equivalence classes of the equivalence relation, the

G

-equivalence classes. Hint. Example 14.1.1:

0

\mathbb{R}^2 \setminus \{0\}

. Example 14.1.2:

X = \{1, 2, 3, 4\}