If G is Isomorphic to H then G is Cyclic iff H is Cyclic Proof

[@goofydog07]

Crystal clear. Well taught

[@TheMathSorcerer]

goofydog07 Thank you!!

[@euler4461]

Let Q be the group of rationals under addition. Then show that any finitely generated subgroup of Q is cyclic.

[@oscarbates2528]

Thank you so much! Quick question: what allows us to say that Φ(g^n)=(Φ(g))^n?

[@TheMathSorcerer]

Note ph(g*g) = phi(g)phi(g) = (phi(g))^2 b/c phi is a group homomorphism,, then you can generalize this for any n, phi(g*...*g) = ph(g)*...*phi(g) = (phi(g))^n

[@TheMathSorcerer]

woops missed a step, for clarity, phi(g^n) = phi(g*...*g) = ph(g)*...*phi(g) = (phi(g))^n, there we go:)

[@khbye2411]

thank you!

[@TheMathSorcerer]

You're welcome!

[@TheMathSorcerer]

[@lyzerbautista6513]

How did pi(g^n) become (pi(g)^n)?

[@jaimedeguzman4762]

same

[@intrepidski9417]

Same

[@euler4461]

Hello sir,
Sir please make a video of this question please