  For an abelian totally real number field $F$ and an odd prime number $p$
which splits totally in $F$, we present a functorial approach to special
"$p$-units" previously built by D. Solomon using "wild" Euler systems. This
allows us to prove a conjecture of Solomon on the annihilation of the $p$-class
group of $F$ (in the particular context here), as well as related annihilation
results and index formulae.
