Is $\Bbb Z/30\Bbb Z $ isomorphic to $\Bbb Z/2\Bbb Z \oplus \Bbb Z/3\Bbb Z \oplus \Bbb Z/5\Bbb Z $?
my reasoning for thinking this isn't the case is that the first group has an element of order 6 whereas the second doesn't.
2026-04-05 18:40:36.1775414436
Is $\Bbb Z/30\Bbb Z $ isomorphic to $\Bbb Z/2\Bbb Z \oplus \Bbb Z/3\Bbb Z \oplus \Bbb Z/5\Bbb Z $?
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Yes: the element $(1,1,1)$ of the latter group has order $30$, so the latter group is a cyclic group of order $30$.