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In article <81qle11mbj2oaplflfi7ouqfut9m4afekh@xxxxxxx>,
Brian VanPelt <bvanpelt@xxxxxxxxxx> writes:
>On 29 Jul 2005 18:20:38 -0700, "ADH" <adoug48@xxxxxxxxxxx> wrote:
>
>>a.) If G is a finite group with fewer than 100 elements and G has
>>subgroups of orders 10 and 25, what is the order of G?
>>b.) Let x and y belong to a group G. Assume x not equal to e (the
>>identity), |y|=2, and yxy^(-1)=x^2. find the order of G.
>>I have no idea where to begin-beginner mathematician.
>
>I saw that someone answered the first question, so I will talk about
>part (b).
>
>I am not certain what you are referring to, so I will guess that G is
>generated by x and y, where y has order 2 and you have the relation
My guess is that the question was find the order of x, rather than
find the order og G.
Derek Holt.
>y x y^-1 = x^2.
>
>Then, using that equation we have
>
>( y x y^-1 ) ( y x y^-1 ) = x^2 x^2
>
>So,
>
>y x ( y^-1 y ) x y^-1 = x^4
>
>y x^2 y^-1 = x^4
>
>But
>
>x^2 = y x y^-1
>
>so
>
>y x^2 y^-1 = x^4
>
>is the same as
>
>y ( y x y^-1 ) y^-1 = x^4
>
>y^2 x y^-2 = x^4
>
>Since the order of y is 2, this last equation reduces to
>
>x = x^4
>
>Thus, x^3 = e, and since x is not the identity element, the order of x
>is 3. So, if I am correct and G is generated by x and y, where x has
>order 3 and y has order 2. What can you say about G?
>
>Brian
>
>
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