Let G = (a) be a cyclic group of order 80. (a) How many subgroups of order 10 are there in G? List them. (b) How many elements of order 10 are there in G? List them. (c) Answer parts (a) and (b) again for subgroups and elements of order 7.

Let G = (a) be a cyclic group of order 80. (a) How many subgroups of order 10 are there in G? List them. (b) How many elements of order 10 are there in G? List them. (c) Answer parts (a) and (b) again for subgroups and elements of order 7.

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 30E: Let G be an abelian group of order 2n, where n is odd. Use Lagranges Theorem to prove that G...

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Question

Let G = (a) be a cyclic group of order 80.
(a) How many subgroups of order 10 are there in G? List them.
(b) How many elements of order 10 are there in G? List them.
(c) Answer parts (a) and (b) again for subgroups and elements of order 7.

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