- #1
mathmari
Gold Member
MHB
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Hey! ![Eek! :eek: :eek:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Show that a cyclic group with only one generator can have at most two elements.
I thought the following:
When $a \neq e$ is in the group, then $a^{-1}$ is also in the group.
So, when $a$ is a generator, then $a^{-1}$ is also a generator.
Is this correct?? (Wondering)
But I how can I use this to show that a cyclic group with only one generator can have at most two elements??
Or should I use something else to prove this?? (Wasntme)
Show that a cyclic group with only one generator can have at most two elements.
I thought the following:
When $a \neq e$ is in the group, then $a^{-1}$ is also in the group.
So, when $a$ is a generator, then $a^{-1}$ is also a generator.
Is this correct?? (Wondering)
But I how can I use this to show that a cyclic group with only one generator can have at most two elements??
Or should I use something else to prove this?? (Wasntme)