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Old 2019-10-29, 16:42   #7
R.D. Silverman
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Nov 2003

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Originally Posted by Dr Sardonicus View Post
Yes, there are cyclic groups of all positive integer orders. The cyclic groups of prime order are the only (nontrivial) simple cyclic groups. Which reminds me...

"Simple Groups", to the tune of "Sweet Betsy from Pike"; words by Saunders Mac Lane

Be it noted, the classification of finite simple groups was achieved in 1981.
This reminds me of a joke that I heard a long time ago.

I was taking an algebra course from Birkhoff. He was introducing the notion of
simple groups. He stated (more or less)

A simple group is one with no self conjugate subgroups... Simple, isn't it???
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