Question

find all subgroups of order 4 of group z2×z2​

Answer 1

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Step-by-step explanation:

The Klein 4-group consists of three elements of order 2 and the identity, and it is up to isomorphism the only group with these properties. As the sentence quoted below your question explains, once you've chosen two such elements, you get the third as sum of the two you've chosen. It is not hard to show that for any two order-2 elements x and y, the set {0,x,y,x+y} indeed is a subgroup isomorphic to the Klein 4-group, and of course any such group has to be of that form.