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group theory, the Fitting subgroup F of a finite group G, named after Hans Fitting, is the unique largest normal nilpotent subgroup of G. Intuitively...

form a subgroup called the torsion subgroup. Cartan subgroup Fitting subgroup Fixed-point subgroup Fully normalized subgroup Stable subgroup Gallian...

group is of characteristic 2 type if the generalized Fitting subgroup F*(Y) of every 2-local subgroup Y is a 2-group. As the name suggests these are roughly...

a p ⟩ {\displaystyle \Phi (G)=\left\langle a^{p}\right\rangle } . Fitting subgroup Frattini's argument Socle Frattini, Giovanni (1885). "Intorno alla...

with the minimal normal soluble subgroups generates a subgroup called the generalized Fitting subgroup. The quasisimple groups are often studied alongside...

Frobenius group. The subgroup of a Zassenhaus group fixing a point is a Frobenius group. Frobenius groups whose Fitting subgroup has arbitrarily large...

trivial subgroup. Subgroup series can simplify the study of a group to the study of simpler subgroups and their relations, and several subgroup series...

theorem Fitting subgroup Generalized Fitting subgroup Hamiltonian group Identity element Lagrange's theorem Multiplicative inverse Normal subgroup Perfect...

Fitting, due to his investigations of nilpotent normal subgroups. A Fitting chain (or Fitting series or nilpotent series) for a group is a subnormal series...

and products of subnormal subgroups. For any Fitting class F, both the subnormal F-subgroups and the normal F-subgroups form lattices. This generalizes...

Fitting's theorem is a mathematical theorem proved by Hans Fitting. It can be stated as follows: If M and N are nilpotent normal subgroups of a group G...

one of the definitions of the Fitting subgroup of a finite group. Similarly, the p′-core is the largest normal subgroup of G whose order is coprime to...

theory) Subgroup Coset Normal subgroup Characteristic subgroup Centralizer and normalizer subgroups Derived group Frattini subgroup Fitting subgroup Classification...

group theory. He proved Fitting's theorem and Fitting's lemma, and defined the Fitting subgroup in finite group theory and the Fitting decomposition for Lie...

subgroups can differ. The subgroup generated by the union of infinitely many normal nilpotent subgroups need not itself be nilpotent, so the Fitting subgroup...

field of group theory, a subgroup of a group is said to be ascendant if there is an ascending series starting from the subgroup and ending at the group...

field of group theory, a subgroup of a group is said to be descendant if there is a descending series starting from the subgroup and ending at the group...

and is the generalization of the Fitting subgroup to groups without the ascending chain condition on normal subgroups. A locally nilpotent ring is one...

GF(2)-type is a group with an involution centralizer whose generalized Fitting subgroup is a group of symplectic type (Gorenstein 1982, definition 1.45). As...

involves studying a maximal subgroup M containing the centralizer of an involution, and its generalized Fitting subgroup F*(M). One succinct version of...