  Let $F$ be a number field unramified at an odd prime $p$ and $F_\infty$ be
the $\mathbf{Z}_p$-cyclotomic extension of $F$. Generalizing Kobayashi
plus/minus Selmer groups for elliptic curves, B\"uy\"ukboduk and Lei have
defined modified Selmer groups, called signed Selmer groups, for certain
non-ordinary $\mathrm{Gal}(\overline{F}/F)$-representations. In particular,
their construction applies to abelian varieties defined over $F$ with good
supersingular reduction at primes of $F$ dividing $p$. Assuming that these
Selmer groups are cotorsion $\mathbf{Z}_p[[\mathrm{Gal}(F_\infty/F)]]$-modules,
we show that they have no proper
sub-$\mathbf{Z}_p[[\mathrm{Gal}(F_\infty/F)]]$-module of finite index. We
deduce from this a number of arithmetic applications. On studying the
Euler-Poincar\'e characteristic of these Selmer groups, we obtain an explicit
formula on the size of the Bloch-Kato Selmer group attached to these
representations. Furthermore, for two such representations that are isomorphic
modulo $p$, we compare the Iwasawa-invariants of their signed Selmer groups.
