I have a (probably) stupid question. I'm in an intro to group theory class and I am trying to better grasp the concept of element order. My question is if I have a group and it has an element of order 3 (or anything finite), can this group also have an element of infinite order? This isn't a homework problem, just trying to grasp basic concepts. I know elements of say a cyclic group have finite order and I know in an infinite group 'I' has order 1, but what about non trivial element orders? I feel stupid for asking this in such a public forum, but I'm also quite curious. No hurry and thank you for your input.
2026-04-06 13:10:39.1775481039
A group with an element of finite order and another element of infinite order?
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