You guys are awesome, by the way, I do have another question :
G is finite group and H, K are subgroups of G, of order 12 and 30 respectively. ( it means that |H|=12, |K|=30- where |H| means the order of H ). Which of the following
can not be the order of subgroup of group generated by H and K
A. 30
B. 60
D. 120
E. infinite countable
we know that |<H,G>| = (|H||G|) /( |H
intersection G| )
where <H,G> is the group generated by H and G
since |H|=3.2.2 and | G| =2.3.5
so if L=H intersection G then |L| is in {1,2, 3, 6 }
and I get stuck
For me, it seems true that the answer is E but the official answer is A
if some know, please explain . Thanks so much