i need the answer quickly 2. Determine the number of elements of order 15 in the group Z75 Z20- Also determine thenumber of cyclic subgroups of order 15 in this group. Is the group Z,5 O Z20 isomorphic tothe group Z25 O Z60? Justify your answer.

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Answered: 2. Determine the number of elements of…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 30E: Exercises 30. For an arbitrary positive integer, prove that any two cyclic groups of order are...

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2. Determine the number of elements of order 15 in the group Z75 ZL20- Also determine the number of cyclic subgroups of order 15 in this group. Is the group Z75 O Z20 isomorphic to the group Z25 O Z6o? Justify your answer.