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Math Help - Lagranges Theorem

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    Lagranges Theorem

    Prove Lagranges Theorem - the order of every subgroup H of a finite group G of order n is a divisor of n.
    Show that the set G = {1,-1,i,-i} (i - (sqrt of -1))
    forms a group with respect to multiplication of complex numbers.Obtain a non trivial subgroup h, justifying your choice and use it to illustrate Lagranges Theorem
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    Quote Originally Posted by asingh88 View Post
    Prove Lagranges Theorem - the order of every subgroup H of a finite group G of order n is a divisor of n.
    Look in a math book? Show that cosets partition the group G and then show that f:H\mapsto aH given by h\mapsto ah is a bijection. Then conclude that \left|G\right|=\left|H\right|\left[G:H\right] where \left[G:H\right] is the number of cosets formed by H.

    Show that the set G = {1,-1,i,-i} (i - (sqrt of -1))
    forms a group with respect to multiplication of complex numbers.Obtain a non trivial subgroup h, justifying your choice and use it to illustrate Lagranges Theorem
    With equal ease show that \mathcal{Z}_n=\left\{z\in\mathbb{C}:z^n=1\right\} is a group (looking at it like that is even easier). If this group were to have a group it would have to be a divisor of 4 and thus is either 1,2,4...but since the subgroup a non-trivial (assumed proper) it must be 2...finish it.
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