  For impartial games $\Gamma$ and $\Gamma'$, the Sprague-Grundy function of
the disjunctive sum $\Gamma + \Gamma'$ is equal to the Nim-sum of their
Sprague-Grundy functions. In this paper, we introduce $p$-calm subtraction
games, and show that for $p$-calm subtraction games $\Gamma$ and $\Gamma'$, the
Sprague-Grundy function of a $p$-saturation of $\Gamma + \Gamma'$ is equal to
the $p$-Nim-sum of the Sprague-Grundy functions of their $p$-saturations. Here
a $p$-Nim-sum is the result of addition without carrying in base $p$ and a
$p$-saturation of $\Gamma$ is an impartial game obtained from $\Gamma$ by
adding some moves. It will turn out that Nim and Welter's game are $p$-calm.
Further, using the $p$-calmness of Welter's game, we generalize a relation
between Welter's game and representations of symmetric groups to disjunctive
sums of Welter's games and representations of generalized symmetric groups;
this result is described combinatorially in terms of Young diagrams.
