TITLE: Nilpotence in the Steenrod Algebra
AUTHOR: Ken Monks
Department of Mathematics
University of Scranton
Scranton, PA 18510
email: monks@uofs.edu
FILENAME: nilpaper.dvi
ABSTRACT:
An infinite family of subalgebras of the mod 2 Steenrod algebra and
isomorphisms between them are constructed. The isomorphisms are used to
produce infinite families of elements having the same nilpotence. Strong
upper and lower bounds for the nilpotence of Milnor basis elements in these
subalgebras are computed. Comparing these bounds and extending to the
families produced via the isomorphisms shows that $\Sq(2^m(2^k-1)+1)$ has
nilpotence $k+2$ for all $m\ge 1$, $k\ge 0$. Finally a strong lower bound
for the nilpotence of $\Pst$ is computed for all $s,t\in\N$.