Let G be a group, and let H < G. Assume that the number of elementsin H is half of the number of elements in G.(a) How many right cosets does H have in G?(b) If x E G, show that x2 E H.(c) Let g E G with o(g) = 3. Show that g E H.

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Answered: Let G be a group, and let H < G. Assume…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 31E: Exercises 31. Let be a group with its center: . Prove that if is the only element of order in ,...

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Let G be a group, and let H < G. Assume that the number of elements in H is half of the number of elements in G. (a) How many right cosets does H have in G? (b) If x E G, show that x2 E H. (c) Let g E G with o(g) = 3. Show that g E H.