Which of the following is a subgroup of the group G = 1, 2, 3, 4, 5, 6 under otimes7 ?

Question

Which of the following is a subgroup of the group G = 1, 2, 3, 4, 5, 6 under otimes7 ? (A)  2, 6, 1  (B)  1, 2, 4  (C)  5, 4, 2  (D)  2, 3 , 1

Tardigrade Admin · Accepted Answer

G = 1, 2, 3, 4, 5, 6 ⊕7 (a) 2, 6, 1) is not a subgroup ∵ 2⊕7 6=5 ∉ 2,6, 1 (b) 1, 2, 4 is a subgroup ∵ it satisfies all properties of group. 1⊕7 2=2, 2 ⊕7 4=1,4 ⊕7 1=4 (c) 5, 4, 2 is not a subgroup · ∵ In this set identity element do not exist. (d) 2, 3, 1 is not a subgroup ∵ 2 ⊕7 3 = 6 ∉ 2, 3, 1

Q. Which of the following is a subgroup of the group $G = {1, 2, 3, 4, 5, 6}$ under $\otimes_{7}$ ?

${2, 6, 1}$

${1, 2, 4}$

${5, 4, 2}$

${2, 3, 1}$

Q. Which of the following is a subgroup of the group G={1,2,3,4,5,6} under ⊗7​ ?

{2,6,1}

{1,2,4}

{5,4,2}

{2,3,1}

Q. Which of the following is a subgroup of the group $G = {1, 2, 3, 4, 5, 6}$ under $\otimes_{7}$ ?

${2, 6, 1}$

${1, 2, 4}$

${5, 4, 2}$

${2, 3, 1}$