Which of the following are subgroups of the group Z×11: {1,3,4,5,9}, {1,3,5,7,8}, {1,8}, {1,10}, {1,3,10}
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Which of the following are subgroups of the group Z×11:
{1,3,4,5,9}, {1,3,5,7,8}, {1,8}, {1,10}, {1,3,10}.
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- Exercises 10. Find an isomorphism from the multiplicative group to the group with multiplication table in Figure . This group is known as the Klein four group. Figure Sec. 16. a. Prove that each of the following sets is a subgroup of , the general linear group of order over . Sec. 3. Let be the Klein four group with its multiplication table given in Figure . Figure Sec. 17. Show that a group of order either is cyclic or is isomorphic to the Klein four group . Sec. 16. Repeat Exercise with the quaternion group , the Klein four group , and defined byIf a is an element of order m in a group G and ak=e, prove that m divides k.Exercises 19. Find cyclic subgroups of that have three different orders.