Question

Which of the following is a subgroup of the group $G=\{1,2,3,4,5,6\}$ under ${\otimes }_7$.

(${\otimes }_7$: under multiplication modulo 7)

• A. $\{2,6,1\}$
• B. $\{1,2,4\}$
• C. $\{5,4,2\}$
• D. $\{2,3,1\}$

Answer 1

The correct option is B $\{1,2,4\}$

(c) can not be a subgroup as identity ${}^{\prime }{1}^{\prime }$ is not present
(d) can not be a subgroup of $2{\otimes }_{7}3=6\text{/}ϵ\{1,2,3\}$
(a) can not be a subgroup as $2{\otimes }_{7}6=5\text{/}ϵ\{2,6,1\}$
$\therefore$ (b) is a subgroup