Let $G$ be a group and let $H$ and $K$ be two subgroups of $G$. If both $H$ and $K$ have $12$ elements, which of the following numbers cannot be the cardinality of the set $HK = \left\{hk : h \in H, k \in K\right\}$?
explanation cardinality of set HK= 144 (H=12 ,K=12)
and subgroup is the divisor of the group so that
1:144/72=2
3:144/36=4
4:144/48=3
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