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October 22

What is the relationship between the order of a conjugacy and the order of elements in that conjugacy class?

A group of order 21 contains a conjugacy class C(x) of order 3. What is the order of x. --150.203.114.14 (talk) 14:30, 22 October 2012 (UTC)

The size of the conjugacy class of x equals the index [G:C_G(x)] of its centralizer. You can easily determine the order of x from this fact.—Emil J. 16:05, 22 October 2012 (UTC)

So, 7 then. Thanks. This question may be a bit trickier: the class equation of a group (order 20) is 1+4+5+5+5. Does this group have a subgroup of order 5? If so, is it normal? --130.56.90.212 (talk) 00:06, 23 October 2012 (UTC)

enumerating a group

I've heard that the Todd–Coxeter algorithm has the useful side-effect of enumerating a group defined by a set of generators. Unfortunately I can't make sense of that description of the algo. Can someone point to a clearer description, or sample code (say in Python or pseudocode)? —Tamfang (talk) 19:08, 22 October 2012 (UTC)