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In reply to a question by K. Dennis, J. Neubueser wrote:

> for all sporadic groups. Can one perhaps use character theory also for

> verifying C_2 or C_3? I have no idea, so here is another question. If

> so, we have plenty of charactertables and tools for handling them in

> GAP.

I don't think it is that easy to use character theory to verify C_2 or

higher. Character theory gives results "up to conjugacy in G", which is

sufficient for C_1, but not for C_2. A character theoretic verification

of C_1 essentialy verifies that for given x_1 there is a conjugacy class

(z) in G such that x_1 is in (z^-1)(z). Clearly , C_1 follows from this.

For given x_1, x_2, there is hope to find a conjugacy class (z) such that

x_1 and x_2 both are in (z^-1)(z), but this doesn't prove C_2, because you

don't know if it is "the same z" you get this way for writing x_1 and x_2

as commutators.

Nevertheless, GAP has been a very useful experimental tool for finding the

conjugacy class (z) in my thesis, and for a verification of C_2 or higher,

character theory will show you which conjugacy classes may contain the

wanted element z and which can't.

Oliver Bonten

--

Heute hack ich, morgen crack ich, uebermorgen hol ich mir dem SysOp sein Login.

Ach wie gut dass niemand weiss, dass ich oli@math.rwth-aachen.de heiss.

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