A group is an algebraic structure consisting of a set of elements together with an operation that satisfies four conditions: closure, associativity, identity and invertibility. Group theory studies groups.

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Inducing representation for groups of order $p^3$

For groups $G$ such that $|G|=p^3$ one can show that $(1)$ $Z=Z(G)\cong C_p$ $(2)$ $G'=Z$ $(3)$ $G/Z \cong C_p \times C_p$ Take any $x \in G/Z$. Then $N=\langle x,Z \rangle$ is an abelian normal ...