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realizing p-groups regularly

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Kevin Oh

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Oct 15, 2009, 11:27:17 AM10/15/09
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Is anyone familiar with the developement of regular inverse Galois
problem? Are all finite p-groups realizable regularly over Q(T)?

It is known that for a finite group to be realizable regularly over Q
(T), a necessary condition called the branch cycle lemma must hold. Is
it true that all finite groups have the property required by branch
cycle lemma?

Kevin

Peter Mueller

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Oct 19, 2009, 6:16:27 AM10/19/09
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> Is anyone familiar with the developement of regular inverse Galois
> problem? Are all finite p-groups realizable regularly over Q(T)?

Regular realization of p-groups over Q(T) are still far out of reach.

> It is known that for a finite group to be realizable regularly over Q
> (T), a necessary condition called the branch cycle lemma must hold. Is
> it true that all finite groups have the property required by branch
> cycle lemma?

The branch cycle lemma is a certain necessary condition for a generating
system of the Galois group. It is a trivial exercise to show that each
finite group has a generating system which fulfills this necessary
condition.

-- Peter M"uller (W"urzburg)

Kevin Oh

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Oct 25, 2009, 5:00:01 PM10/25/09
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On Oct 19, 6:16�pm, Peter Mueller <peter.muel...@mathematik.uni-

The branch cycle lemma does not require the conjugacy classes
associated to the generators to be distinct. Is it still obvious that
all finite groups have this property together with the requirement
that the conjugacy classes associated to the generators are distinct?

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