  In this paper, we compare the structure of Selmer groups of certain classes
of Galois representations over an admissible $p$-adic Lie extension. Namely, we
show that the $\pi$-primary submodules of the Pontryagin dual of the Selmer
groups of two Galois representations have the same elementary representations
when the two Galois representations in question are either Tate dual to each
other or are congruent to each other. In the first situation, our result gives
a partial answer to the question of Greenberg on whether the Pontryagin dual of
the Selmer groups of two Galois representations that are Tate dual to each
other are pseudo-isomorphic (up to a twist of the Iwasawa algebra). In the
second situation, our result will be applied to study the variation of the
$\pi$-primary submodules of the dual Selmer groups of certain specialization of
a big Galois representation. One of the important ingredient in our proofs is
an asymptotic formula for $\pi$-primary modules over a noncommutative Iwasawa
algebra which can be viewed as a generalization of a weak analog of the
classical Iwasawa asymptotic formula.
