# Tag Info

## Hot answers tagged group-actions

### Intuitive meaning of transitive group action.

Let us consider a group action of $G$ on a set $X$ defined by $(g, x) =g\star x$ Let $x\in X$ , then orbit of $x$ is defined as $\mathcal{O}_x=\{g\star x:g\in G\}$ Claim: The relation $\sim$ on $X$ ...
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### How many transitive actions does the quaternion group have, up to isomorphism?

Hint Just like in your previous post about transitive actions of $C_{12}$, the general result (that @Derek Holt clued us in on) is that there are as many inequivalent actions as conjugacy classes of ...
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Here is an answer for the reformulated question (requiring effectiveness) but which might be considered as exploring a loophole. Further reformulations are welcome, but for now, here we go: For each $... • 17.6k 1 vote ### Group Operations/ Group Actions When you have a group$G$acting on a set$X$(a so-called$G$-set), you get a homomorphism from$G$into$S_X$, the symmetric group on$X\$. Any group acts on itself by left (or right) multiplication. ...
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