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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 9

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NOTE that $Z_{n}$ is a cyclic group, hence an abelian group.
For any group, we know by Lagrange's theorem that the order of subgroup divides the order of the group.

For abelian groups, the converse of Lagrange's theorem is also true. For the Abelian group, we know that if $d$ divides the order of the group then there exists a subgroup of size $d.$

The subgroups of $Z_9$ are:

  1. $\{0\},$
  2. $\{0, 3, 6\},$
  3. $Z_{9}.$
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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 $2$
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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