User haha tell me a noether one - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T18:55:46Z http://mathoverflow.net/feeds/user/9286 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/39315/classification-of-small-complete-groups classification of small complete groups Haha tell me a Noether one 2010-09-19T16:51:50Z 2010-10-01T01:26:00Z <p>This is "escalated" from <a href="http://math.stackexchange.com/questions/4498/classification-of-small-complete-groups" rel="nofollow">stackexchange</a>. </p> <p>So, $S_n$ for $n \ne 2,6$, $\text{Aut}(G)$ for $G$ non-cyclic simple, $\text{Hol}(C_p)$ for $p$ odd prime are well-known classes of complete group. </p> <p>What's the smallest complete group not in these classes? What's a possible way to generalise that group, and what's the smallest complete group not in that class either? And so on. I'd be interested in any partial result.</p> http://mathoverflow.net/questions/38856/jokes-in-the-sense-of-littlewood-examples/39038#39038 Answer by Haha tell me a Noether one for Jokes in the sense of Littlewood: examples? Haha tell me a Noether one 2010-09-17T00:18:45Z 2010-09-17T00:25:34Z <p>Nobody mentioned the <a href="http://en.wikipedia.org/wiki/third_isomorphism_theorem" rel="nofollow">third isomorphism theorem</a> yet? If $B$ and $C$ are normal subgroups of $A$ and $C \le B$ then $\frac{A/C}{B/C} \cong \frac{A}{B}$.</p> http://mathoverflow.net/questions/39315/classification-of-small-complete-groups Comment by Haha tell me a Noether one Haha tell me a Noether one 2010-09-26T22:37:10Z 2010-09-26T22:37:10Z I've downloaded it and am just getting used to it. There doesn't seem to be an IsCompleteGroup(). I have come up with IsTrivial(Center(G)) and Order(G) = Order(AutomorphismGroup(G)). Is there a more efficient way?