Let G be a group and H be a subgroup ofG=<a> if|G|=36andH=<a^4>. How do you find |H| ?

1 Answer
Jan 18, 2018

abs(H) = 9

Explanation:

If I understand your notation correctly, G is a multiplicative group generated by one element, namely a.

Since it is also finite, of order 36 it can only be a cyclical group, isomorphic with C_36.

So (a^4)^9 = a^36 = 1.

Since a^4 is of order 9, the subgroup H generated by a^4 is of order 9.

That is:

abs(H) = 9