Let V4 denote the Klein 4-group: that is V4 = {1, a, b, c} where a = (1 2)(3 4), b = (1 3)(2 4) and c = (1 4)(2 3) (permutations of four points). Find three distinct subgroups H1, H2 and H3 of V4 of order 2. Show that Hi ∩ Hj = 1 for all i %= j and V4 = HiHj for all i and j. [Note that I am using the more conventional notation V4 for the Klein 4-group, rather than the less frequently used K4 from MT4003. Here V stands for Viergruppe.]

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Representation of Polynomial

It is necessary for the polynomial expression that each expression consists of two parts: