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  3. 4.- show the solution: a.- let g be a group, h a s

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

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Advance Math

4.- Show the solution:

a.- Let G be a group, H a subgroup of G and a?G. Prove that thecoset 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 ofpermutations.

SUBJECT: Abstract Algebra

(18,19,20)

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