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, so that it can be represented as the pairs {(0,0), (0,1), (1,0), (1,1)}} under component-wise addition modulo 2 (or equivalently the bit strings {00, 01, 10, 11}}under bitwise XOR), with (0,0) being the group's identity element. The Klein four-group is thus an example of an elementary abelian 2-group, which is also called a Boolean group.

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