- #1

- 10

- 0

## Homework Statement

A group G acts transitively on a non empty G-set S if, for all s1, s2 in S, there exists an element G in G such that g*s1 = s2. Characterize transitive G-set actions in terms of orbits. Prove your answer

## Homework Equations

Transitive G-set Actions: for all s1, s2 in S, there exists a g in G such that g*s1=s2

Regular G-set Actions: 1) (gh)s = g(hs)

2) 1s = s

Orbit of S = {s' in S such that s' in gs for some g in G}

## The Attempt at a Solution

Past the definitions, i don't really know anything. The problem is vague and it seems like I'm supposed to write the definition of transitive G-set actions in terms of orbits, but i don't know how to do that nor do i know how i would "prove" that.

Tips are greatly appreciated :D.