  Quandle colorings and cocycle invariants are studied for composite knots, and
applied to chirality and abelian extensions. The square and granny knots, for
example, can be distinguished by quandle colorings, so that a trefoil and its
mirror can be distinguished by quandle invariants of composite knots. We
investigate this and related phenomena. Quandle cocycle invariants are studied
in relation to the connected sum, and formulas are given for computing the
cocycle invariant from the number of colorings of composite knots. Relations to
corresponding abelian extensions of quandles are studied, and extensions are
examined for the table of small connected quandles, called Rig quandles.
Computer calculations are presented, and summaries of outputs are discussed.
