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Home Q & A Board Science-Related Homework Help Chemistry (Moderator: Laser_3)
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nurshn nurshn
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11 years ago
If I recall correctly, the order of an element in a group must divide the order of the group. So if the element has infinite order, must the group have infinite order as well? This would make sense since repeated multiplication (or addition) would not ever give the identity, thus generating new, distinct (I think?), elements every time.

Any help please?

Thank you.
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#1
11 years ago
All elements of finite groups must have finite order.  So, yes, if there's an element of infinite order the group must necessarily be infinite.
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