User talk:Cyb3r

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[edit] Alternation group

(Reply to [1])

No problem. As I mentioned in the edit summary, it appears to be a common confusion. Textbooks often explicitly prove A4 is not simple, and A5 is simple, and then An is simple for n≥5, but leave out A1, A2, A3 as being a little too small to say anything about. One might check out list of small groups to see how there are not very many small groups, so they can usually be checked by hand easily enough.

The alternating group A₃ is a group of order 3. Every group of order 3 is a cyclic group of order 3. Every cyclic group of order 3 is isomorphic to A₃. Sometimes one studies a particular cyclic group of order 3, the set {0,1,2} under addition modulo 3, also known as Z/3Z. This group is also isomorphic to A₃. JackSchmidt (talk) 18:19, 31 December 2007 (UTC)