How do I see a group's generator? For example in $\mathbb{Z}_{10}$ ? I'm reading my school book but I don't find any methods.
2026-03-31 08:07:21.1774944441
How do I see a group's generator?
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I suspect you are looking for generating sets - the group $\mathbb{Z}_2\oplus\mathbb{Z}_2$ for example has no single generator, but has generating sets $\{(1,0),(0,1)\}$ for example.
It is not generally immediately obvious what a generating set for a group is. In the case of cyclic groups, $\mathbb{Z}_n$, it is a nice exercise to show that $m\in\mathbb{Z}_n$ is a generator if and only if $\mathrm{gcd}(m,n)=1$. For more general groups you're better off searching for or asking about the specific group.