Which one of the following multiple-choice questions is incorrect? Q 2 Which one of the following is incorrect?(a) {1,2,3} under multiplication modulo 4 is not a group.(b) {1,2,3, 4} under multiplication modulo 5 is a group.(c) The intersection of any two subgroups of a group G is also a subgroupof G.(d) {0, 2,4} under addition modulo 8 is a subgroup of (Zg, Os).Q 3 If a andb are the elements of a group G, then (ba)-1 =(a) b-'a-1(b) a-lb-1(c) a-1b(d) b-laQ 4 The inverse of the element (132) of the group S3 under function composi-tion o is(a) (12)(b) (132)(c) (123)(d) (23)Q 5 The order of the element (123) of the group (S3,0) is(a) 1(b) 2(c) 3(d) o0Q 6 The order of the group (U(12), 12) is(а) 12(b) 11(c) 6(d) 4Q 7 Which one of the following is abelian group?(a) (S3,0)(b) {A e Mnxn : det(A) = 1} under matrix multiplication(c) Any cyclic group(d) None of the above Q 8 Which one of the following is a cyclic group?(a) (Z,+)(b) (Q, +)(c) (R, +)(d) (R \ {0}, ·)Q 9 Which one of the following is the smallest subgroup of (Z, +) that contains2?(a) (2Z, +)(b) (4Z, +)(c) (6Z, +)(d) None of the aboveQ 10 Which one of the following is not a ring?(a) (Z, +, ·)(b) (MAx4(R),+,:)(c) (Z5, O5, 85)(d) None of the above

Name: Which one of the following multiple-choice questions is incorrect? Q 2
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Description: Which one of the following multiple-choice questions is incorrect? Q 2 Which one of the following is incorrect?(a) {1,2,3} under multiplication modulo 4 is not a group.(b) {1,2,3, 4} under multiplication modulo 5 is a group.(c) The intersection of an

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Answered: {1,2, 3} under multiplication modulo 4…

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{1,2, 3} under multiplication modulo 4 is not a group. {1,2, 3, 4} under multiplication modulo 5 is a group. The intersection of any two subgroups of a group G is also a subgroup of G.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 3E: Exercises 3. Find an isomorphism from the additive group to the multiplicative group of units...

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