[Math] In group theory, if G is a group, what does the notation G’ mean


I am currently working my way through Daniel Gorenstein's Book "Finite Groups", learning about transfer and the focal subgroup and the notation G' keeps popping up and I can't seem to figure out what it refers to. I will give you an example of where it's used:
If G possesses a proper normal subgroup K such that G(with a bar on top) = G/K is a p-group, then G(with a bar on top)' is a subset of G(with a bar on top)

Best Answer

The commutator group, $G'=[G,G]=\langle aba^{-1}b^{-1}: a,b\in G\rangle$.

Note that is a normal subgroup of $G$, and $G'$ represent how commutative is the group, ie $G$ is abelian iff $G'=\{1\}$.

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