An element of a Hopf algebra is called grouplike if $\Delta(g)=g\otimes g$.
Let $G$ be a finite group and $k$ be a field. Then the group algebra $kG$ can be made into a Hopf algebra by defining the coproduct by $\Delta(g):=g\otimes g$, the counit by $\varepsilon(g)=1$ and the antipode by $S(g)=g^{-1}$.
For an arbitrary Hopf algebra $H$ an element $h\in H$ is called grouplike if $\Delta(h)=h\otimes h$. It can be shown that in this case $S(h)$ is a multiplicative inverse of $h$. Thus the set of grouplike elements forms a group.
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