Answered: Let |G| = 15. If G has only one…

Let |G| = 15. If G has only one subgroup of order 3 and only one oforder 5, prove that G is cyclic. Generalize to |G| = pq, where p andq are prime.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 15E: Let H1 and H2 be cyclic subgroups of the abelian group G, where H1H2=0. Prove that H1H2 is cyclic if...

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Question

Let |G| = 15. If G has only one subgroup of order 3 and only one of
order 5, prove that G is cyclic. Generalize to |G| = pq, where p and
q are prime.

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