Show that the cyclic group of n objects, Cn, may be represented by r", m =0, 1, 2, ...,n - 1. Here r is a generator given by17.2.5r= exp(2nis/n).The parameter s takes on the values s = 1,2, 3, ..., n, with each value of s yielding adifferent 1-D (irreducible) representation of C.

Given Cn is a cyclic group of n elements To show Cn is generated by some element r of Cn. That is…

Answered: Show that the cyclic group of n…

Show that the cyclic group of n objects, Cn, may be represented by r", m = 0, 1, 2,...,n– 1. Here r is a generator given by r = exp(27 is/n). %3D

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.6: Quotient Groups

Problem 11E: Find all homomorphic images of the quaternion group.

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Show that the cyclic group of n objects, Cn, may be represented by r", m =
0, 1, 2, ...,n - 1. Here r is a generator given by
17.2.5
r= exp(2nis/n).
The parameter s takes on the values s = 1,2, 3, ..., n, with each value of s yielding a
different 1-D (irreducible) representation of C.

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