plural of derived subgroup

plural of commutator subgroup

(group theory) A subgroup H of a group G that is invariant under conjugation; that is, for all elements h of H and for all elements g in G, the element ghg⁻¹ is in H.

plural of Fitting subgroup

(mathematics) For a finite group G: the unique largest normal nilpotent subgroup of G, which intuitively represents the smallest subgroup that "controls" the structure of G when G is solvable.

(algebra) Said of a group acting on a set, and with respect to an element of that set: the subgroup of the given group whose action on the given element of the set that the group acts on leaves that element fixed.

(algebra) Subgroup of an abelian group whose generators have finite order.