4.- Show the solution: a.- Let G be a group, H a subgroup of G and...

4.- Show the solution:

a.- Let G be a group, H a subgroup of G and a∈G. Prove that the coset aH has the same number of elements as H.

b.- Prove that if G is a finite group and a∈G, then |a| divides |G|. Moreover, if |G| is prime then G is cyclic.

c.- Prove that every group is isomorphic to a group of permutations.

SUBJECT: Abstract Algebra

(18,19,20)

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Expert Solution

Colby Messinger answered 1 year ago

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