Source: /cirosantilli/cycle-of-an-element-of-a-group

= Cycle of an element of a group

Take the element and apply it to itself. Then again. And so on.

In the case of a <finite group>, you have to eventually reach the <identity element> again sooner or later, giving you the <order of an element of a group>.

The continuous analogue for the cycle of a group are the <one parameter subgroups>. In the continuous case, you sometimes reach identity again and to around infinitely many times (which always happens in the finite case), but sometimes you don't.