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Found problems: 1

2005 Gheorghe Vranceanu, 1
Tags: group theory , abstract algebra , power set , modulo 2 , boolean algebra , symmetric difference
For a natural number $ n\ge 2, $ prove that the $ \text{n-ary} $ direct product of the group of order $ 2 $ is abelian and isomorphic with the group of the power set of a set under symmetric difference.