Let |G|=pq, where p and q are prime. If G has only one subgroup of order p and only one of order q, prove that G is cyclic.
Let |G|=pq, where p and q are prime. If G has only one subgroup of order p and only one of order q, prove that G is cyclic.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.4: Cosets Of A Subgroup
Problem 29E: Let be a group of order , where and are distinct prime integers. If has only one subgroup of...
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Let |G|=pq, where p and q are prime. If G has only one subgroup of order p and only one of order q, prove that G is cyclic.
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