4. Apply the Lagrange's Theorem in the following exercises: a) Let n be a prime number,...

Transcribed Image Text:

4. Apply the Lagrange's Theorem in the following exercises: a) Let n be a prime number, G be a group of order n, and H be a proper subgroup of G. What can you say about H and its order. Pipps, where P1, P2, and p3 are three b) Let G be a group of order n, with n= different prime numbers. Let H be a proper subgroup of G of order k. How many possible values are there for k? Prove your answers. c) Let G be a group, and H a subgroup pf G. Let |G| = 91 and H|28. What is H? d. Let G be a group of order 8, and let a € G such that no one of the elements a, a², a³, and a equals the identity element. What is the value of the order of d. lal? 4. Apply the Lagrange's Theorem in the following exercises: a) Let n be a prime number, G be a group of order n, and H be a proper subgroup of G. What can you say about H and its order. Pipps, where P1, P2, and p3 are three b) Let G be a group of order n, with n= different prime numbers. Let H be a proper subgroup of G of order k. How many possible values are there for k? Prove your answers. c) Let G be a group, and H a subgroup pf G. Let |G| = 91 and H|28. What is H? d. Let G be a group of order 8, and let a € G such that no one of the elements a, a², a³, and a equals the identity element. What is the value of the order of d. lal?

Answer rating: 100% (QA)

Let s solve our probl... View the full answer