Induced magma power set magma

context	$\langle\!\langle M,* \rangle\!\rangle$ … magma
definiendum	$\langle\!\langle {\mathcal P}M,\star \rangle\!\rangle$
definition	$\star\in$ binary operation on ${\mathcal P}M$
definition	$S\star T:=\{x*y\ \|\ x\in S, y\in T\}$

When talking about left cosets etc., people write $xS$ for $\{x\}S$ .

Wikipedia: Magma