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"ADH" <adoug48@xxxxxxxxxxx> wrote in message
news:1122686438.941239.303820@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> 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?
Lagrange's theorem states that the order of a group must be divisible by the
orders of its subgroups. In your case, the order of the G is <=99. Given
this upper bound, you know that the order of G must also be divisible by 10
and 25. The answer would occur to me as being the LCM of 10 and 25. (2.5.5 =
50)
> 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.
>
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