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Limits of Abelian Subgroups of Finite pgroups J.L. Alperin \Lambda
 

Summary: Limits of Abelian Subgroups of Finite p­groups
J.L. Alperin \Lambda
University of Chicago
alperin@math.uchicago.edu
G. Glauberman y
University of Chicago
gg@math.uchicago.edu
1 Introduction
Abelian subgroups play a key role in the theory and applications of finite
p­groups. Our purpose is to establish some very general results motivated by
special results that have been of use. In particular, it is known [KJ] that if
a finite p­group, for odd p, has an elementary abelian subgroup of order p n ,
n Ÿ 5, then it has a normal elementary abelian subgroup of the same order.
Our first main result is a general one of this type.
Theorem A
If A is an elementary abelian subgroup of order p n in a p­group P , then
there is a normal elementary abelian subgroup B of the same order contained
in the normal closure of A in P , provided that p is odd and greater than
4n \Gamma 7.
We are very grateful to the referee for an improvement to our argument

  

Source: Alperin, Jon L. - Department of Mathematics, University of Chicago

 

Collections: Mathematics