If two groups are residual to a third, every group residual to one is residual to the other. The Gambier extension of this theorem states that if two groups are pseudoresidual
to a third, then every group pseudoresidual to the first with an excess greater than
or equal to the excess of the first minus the excess of the second is pseudoresidual
to the second, with an excess 
.
Group Residue Theorem
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References
Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, pp. 30-31, 1959.Referenced on Wolfram|Alpha
Group Residue TheoremCite this as:
Weisstein, Eric W. "Group Residue Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GroupResidueTheorem.html