Notation for subgroup-defining functions

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This is a notation page: it lists some important notation

For convenience of notation, G here denotes the group on which we are computing the subgroup-defining function.

Subgroup-defining functions

Name of subgroup-defining function Notation for single iteration Notation for n iterations Associated quotient-defining function Notation for single iteration Notation for multiple iterations
Center Z(G) -- (idempotent) Inner automorphism group Inn(G), G/Z(G)  ?
Commutator subgroup, derived subgroup G', [G,G] G^{''''\ldots} n times, or G^{(n)} Abelianization G^{ab} -- (idempotent)
Fitting subgroup F(G) -- (idempotent) Fitting quotient G/F(G) -- (idempotent)
Frattini subgroup \Phi(G) \Phi^n(G) Frattini quotient G/\Phi(G) -- (idempotent)