10.3.3. Let G = Z/4Z × Z/6Z, and let H be the subgroup of G generated by(2,2).(a) What are the elements of H?(b) What are the elements of G/H?(c) Find a familiar group that is isomorphic to G/H.

Given that G=ℤ/4ℤ×ℤ/6ℤ.i.e. G=ℤ4×ℤ6H is a subgroup of G generated by 2,2i.e. H=<2,2> oG=4×6=24

Answered: 10.3.3. Let G Z/4Z x Z/6Z, and let H be…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 28E

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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 of K is 3, what are all the possible orders of H?
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10.3.3. Let G Z/4Z x Z/6Z, and let H be the subgroup of G generated by (2, 2). (a) What are the elements of H? (b) What are the elements of G/H? (c) Find a familiar group that is isomorphic to G/H.