# Definition of “Grouplike”

Hi!  In terms of a nonzero element $x\in \mathbb{F} [G]$ being defined as grouplike,is it sufficient to have one comultiplication such that

$\Delta (x) = x \otimes x$ or does it require that to be true for every comultiplication on the space? Thank you.

1. It should satisfy $\Delta(x) = x\otimes x$ with $\Delta$ being the canonical comultiplication (i. e., the one defined by $\Delta(g) = g\otimes g$ for every $g \in G$. All the other comultiplications don’t matter.