 
Summary: Journal of Pure and Applied Algebra 206 (2006) 5558
www.elsevier.com/locate/jpaa
On a theorem of Mislin
J.L. Alperin
Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, IL 60637, USA
Received 12 October 2004; received in revised form 22 February 2005
Available online 6 September 2005
Dedicated to Eric M. Friedlander on his 60th birthday
Abstract
A theorem of Mislin gives an equivalence between a condition on restriction of cohomology to a
subgroup with an embedding condition on the subgroup. Two variations of this result are proved and
a reduction is given towards a purely algebraic proof of Mislin's original theorem.
© 2005 Elsevier B.V. All rights reserved.
MSC: 20J06
1. Introduction
A celebrated theorem of Mislin [3], using deep homotopy results, shows the equivalence
between a purely cohomological condition and the embedding of a subgroup. Specifically,
let H be a subgroup of a finite group, p a prime and assume that a Sylow psubgroup P of G
lies in H. Let k be a field of characteristic p, e.g. the field of p elements. Mislin shows that
the following two conditions are equivalent:
