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Subhasis Biswas Consider an infinite commutative group $G$. Let $<a_1>, <a_2>, ..., <a_m>$ ($<a_i>=C_i$) be a finite collection of infinite cyclic subgroups of $G$ such that $C_j \not\subset \displaystyle\bigcup_{I \setminus \{j\}}C_i$ , $I=\{1,2,3,...,m\}$. Then $\displaystyle\bigcup_{i=1}^mC_i$ is never a subgroup of $G$.