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A cohomological property of p-groups
Authors:P.?J.?Cameron  mailto:P.J.Cameron@qmul.ac.uk"   title="  P.J.Cameron@qmul.ac.uk"   itemprop="  email"   data-track="  click"   data-track-action="  Email author"   data-track-label="  "  >Email author,T.?W.?Müller  mailto:T.W.Muller@qmul.ac.uk"   title="  T.W.Muller@qmul.ac.uk"   itemprop="  email"   data-track="  click"   data-track-action="  Email author"   data-track-label="  "  >Email author
Affiliation:(1) School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, E1 4NS London, United Kingdom
Abstract:
Let p be a prime, 
$$ frak G $$
a finite p-group, 
$$ frak H $$
any finite group with order divisible by p,and 
$ alpha : frak {G} rightarrow textrm{Aut}(frak {H}) $
any action of 
$$ frak G $$
on 
$$ frak H $$
. We show that the cardinality of the set of all derivations 
$ d : frak {G} rightarrow frak {H} $
with respect to this action is a multiple ofp. This generalises theorems of Frobenius and Hall.Received: 16 June 2003
Keywords:20J06.
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