  In this paper we find a finite set of generators and defining relations for
the singular pure braid group $SP_n$, $n \geq 3$, that is a subgroup of the
singular braid group $SG_n$. Using this presentation, we prove that the center
of $SG_n$ (which is equal to the center of $SP_n$ for $n \geq 3$) is a direct
factor in $SP_n$ but it is not a direct factor in $SP_n$. We introduce
subgroups of camomile type and prove that the singular pure braid group $SP_n$,
$n \geq 5$, is a subgroup of camomile type in $SG_n$. Also we construct the
fundamental singquandle using a representation of the singular braid monoid by
endomorphisms of free guandle. For any singular link we define some family of
groups which are invariants of this link.
