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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 4
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The set $\{1, 2, 3, \dots , n - 1\}$ is a group under multiplication modulo $n.$ Then the smallest value of $n$ between $20$ and $30$ is $(20, 30$ included $)\;$ _______
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We know that the set $\{1, 2, \dots , n - 1\}$ is a group under multiplication modulo $n$ if and only if $n$ is a prime number.
so, the minimum possible value of $n$ between $20$ and $30$ is $23.$
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Here i have taken an example and tried to explain how to make it group under multiplication modulo.
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Answer:
23
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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 2
Let $\text{G}$ is a cyclic group with generator ‘$a$’. Order of ‘$a$’ is $29.$ The number of subgroups $\text{G}$ has ________
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In a group $\text{G},$ every element other than the identity element has order $2$ then $\mathrm{G}$ is? Abelian group Cyclic group Non-abelian group Non-cyclic group
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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 5
Consider the group $0,1,2,3,4,+{ }_{5}$. What will be the value of $2^{-3}$ and $3^{-2}$ for the given group? $1$ and $1$ $2$ and $3$ $4$ and $4$ $3$ and $2$
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