  A solution to the Kervaire invariant problem is presented. We introduce the
concepts of abelian structure on skew-framed immersions, bicyclic structure on
$\Z/2^{[3]}$--framed immersions, and quaternionic-cyclic structure on
$\Z/2^{[4]}$--framed immersions. Using these concepts, we prove that for
sufficiently large $n$, $n=2^{\ell}-2$, an arbitrary skew-framed immersion in
Euclidean $n$-space $\R^n$ has zero Kervaire invariant. Additionally, for $\ell
\ge 12$ (i.e., for $n \ge 4094$) an arbitrary skew-framed immersion in
Euclidean $n$-space $\R^n$ has zero Kervaire invariant if this skew-framed
immersion admits a compression of order 16.
