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In a letter to the GAP-forum Keith Dennis asks various questions about

all elements in a group being commutators of kinds. I cannot provide

any information on his properties C_n for n>1, but I can report that

in his thesis, just finished under the direction of Professor Pahlings

in Aachen, Oliver Bonten has proved that C_1 holds for 'almost all'

simple groups of Lie type. To be more precise, for each series of such

groups with fixed dimension n there is a bound for the order q of the

field involved such that C_1 holds for all groups with q bigger than

this bound. The bounds are very big and no hope to settle the

remaining cases by computer even for small n. The methods of the

proofs are from Character theory - as well as by the way were the

methods by which some years ago we verified by computer that C_1 holds

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.

Joachim Neubueser

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