Answer to Question #203312 in Abstract Algebra for Raghav

Question #203312

If G is a group with o(g) < 100 and G has subgroups of order 10 and 25, what is the

order of G?


1
Expert's answer
2021-06-14T18:10:41-0400

According to Lagrange's theorem for a finite group GG, the order of every subgroup HH of GG divides the order of GG. Let nn be the order of  GG. Then 1010 divides nn and 2525 divides nn. It follows that 50=LCM(10,25)50=LCM(10,25) divides n.n. Taking into account that n<100,n<100, we conclude that n=50.n=50.


Answer: the order of GG is 50.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment