FCJoinDOTs is an option for DotSimplify and other functions that use DotSimplify internally. When set to True, DotSimplify will try to rewrite expressions like A.X.B + A.Y.B as A.(X+Y).B.
Notice that although the default value of FCJoinDOTs is True, the corresponding transformations will occur only if the option Expanding is set to False (default: True)
DeclareNonCommutative[A, B, X, Y]DotSimplify[A . X . B + A . Y . B]A.X.B+A.Y.B
DotSimplify[A . X . B + A . Y . B, FCJoinDOTs -> True]A.X.B+A.Y.B
DotSimplify[A . X . B + A . Y . B, FCJoinDOTs -> True, Expanding -> False]A.(X+Y).B
DotSimplify[GA[mu, 6, nu] + GA[mu, 7, nu], FCJoinDOTs -> True, Expanding -> False]\bar{\gamma }^{\text{mu}}.\left(\bar{\gamma }^6+\bar{\gamma }^7\right).\bar{\gamma }^{\text{nu}}