Let G = Z9 x Z12 × Z16. (a) Find all subgroups of G of order 144. (b) Let H = ((3,3, 6)), the cyclic subgroup of G generated by (3,3,6). Determine |G/H. (c) Determine the order of the element (4,5, 2) + H in the factor group G/H.
Let G = Z9 x Z12 × Z16. (a) Find all subgroups of G of order 144. (b) Let H = ((3,3, 6)), the cyclic subgroup of G generated by (3,3,6). Determine |G/H. (c) Determine the order of the element (4,5, 2) + H in the factor group G/H.
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 12E: Let H and K be subgroups of a group G and K a subgroup of H. If the order of G is 24 and the order...
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Transcribed Image Text:Let G = Z9 x Z12 × Z16.
(a) Find all subgroups of G of order 144.
(b) Let H = ((3,3, 6)), the cyclic subgroup of G generated by (3,3,6). Determine |G/H.
(c) Determine the order of the element (4,5, 2) + H in the factor group G/H.
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