Thread: 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

Originally Posted by asingh88

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 and then show that given by is a bijection. Then conclude that where is the number of cosets formed by .

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 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 and thus is either ...but since the subgroup a non-trivial (assumed proper) it must be ...finish it.