62 476
Assignments Done
98,8%
Successfully Done
In June 2018

Answer to Question #17371 in Abstract Algebra for steve peters

Question #17371
Let f:G1-->G2 be a homomorphism of groups. Let H be a cyclic subgroup of G1. Prove the f(H) is a cyclic subgroup of G2.
Expert's answer
If H cyclic then exist g from H generator element suchthat every element h from H h=g^n for some natural n
f(H)={f(h) | h belongs to H}={f(g^n)|n - natural}= | f -homomorphism so |= { (f(g))^n | n - natural}
f(H) is a subgroup of G2 and it is generated by f(g) soit is cyclic

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 first!

Leave a comment

Ask Your question

Submit
Privacy policy Terms and Conditions