THE HIT PROBLEM OF RANK FIVE IN AGENERIC DEGREE

Abstract

Let
E
k
be an elementary abelian 2-group of rank
k
and let
BE
k
be
the classifying space of
E
k
. Then,
P
k
:=
H
∗
(
BE
k
)
∼
=
F
2
[
x
1
, x
2
, . . . , x
k
]
,
a polynomial algebra in
k
generators
x
1
, x
2
, . . . , x
k
, with the degree of
each
x
i
being 1. This algebra is regarded as a module over the mod-
2
Steenrod algebra,
A
.
We study the
Peterson hit problem
of finding a minimal set of gener-
ators for
A
-module
P
k
. It is an open problem in Algebraic Topology. In
this paper, we explicitly determine a minimal set of
A
-generators for
P
5
in terms of the admissible monomials for the case of the generic degree
m
= 2
d
+2
+ 2
d
+1
−
3
with
d
⩾
6