Suppose $G$ is a group and $H_1, H_2\leq G$ such that $H_1\cup H_2=G.$

How can I prove that either $G=H_1$ or $G=H_2$?

  • $\begingroup$ Suppose both were proper subgroups. Choose $g_i \in G\setminus H_i$, then ... $\endgroup$ Feb 22, 2014 at 0:03
  • $\begingroup$ I'm confused - such that $H_1\cup H_2$ what? $\endgroup$
    – user122283
    Feb 22, 2014 at 0:05
  • $\begingroup$ Prove that $H_1 \cup H_2$ is a subgroup of $G$ if and only if $H_1 \subset H_2$ or $H_2 \subset H_1$ $\endgroup$
    – dani_s
    Feb 22, 2014 at 0:10


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