in the area of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is mapped to itself by every automorphism of the parent...

In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation...

specific domains Characteristic polynomial, a polynomial associated with a square matrix in linear algebra Characteristic subgroup, a subgroup that is invariant...

examples section). If A is abelian, then the torsion subgroup T is a fully characteristic subgroup of A and the factor group A/T is torsion-free. There...

want to prove that C is contained in H. If not, pick a minimal characteristic subgroup M/Z(H) of C/Z(H), where Z(H) is the center of H, which is the same...

form a subgroup of index 2 in S, called the alternating subgroup A. Since A is even a characteristic subgroup of S, it is also a normal subgroup of the...

commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group. The commutator subgroup is important...

The center is a normal subgroup, Z(G) ⊲ G, and also a characteristic subgroup, but is not necessarily fully characteristic. The quotient group, G /...

(where I is the identity matrix) is a normal subgroup and even a characteristic subgroup of O(n), and, if n is even, also of SO(n). If n is odd, O(n) is...

a group is said to be characteristically simple if it has no proper nontrivial characteristic subgroups. Characteristically simple groups are sometimes...

commute with every element of the group. The center is a characteristic subgroup. A subgroup H {\displaystyle H} of G {\displaystyle G} is termed central...

particular characteristic subgroups of a Sylow p-subgroup. Glauberman improved this further by showing that one only needs to use one characteristic subgroup: the...

the Puig subgroup, introduced by Puig (1976), is a characteristic subgroup of a p-group analogous to the Thompson subgroup. If H is a subgroup of a group...

{\displaystyle \Phi (G)} is always a characteristic subgroup of G; in particular, it is always a normal subgroup of G. If G is finite, then Φ ( G ) {\displaystyle...

slightly different. Antiautomorphism Automorphism (in Sudoku puzzles) Characteristic subgroup Endomorphism ring Frobenius automorphism Morphism Order automorphism...

subgroup A subgroup of a group is a central subgroup of that group if it lies inside the center of the group. characteristic subgroup A subgroup of a group...

Hungarians can be divided into several subgroups according to local linguistic and cultural characteristics; subgroups with distinct identities include the...

of any given Sylow 2-subgroup. If this condition holds for all maximal 2-local subgroups M then G is said to be of characteristic 2 type. Gorenstein, Lyons...

theory, the Thompson subgroup J ( P ) {\displaystyle J(P)} of a finite p-group P refers to one of several characteristic subgroups of P. John G. Thompson (1964)...

normal p-subgroup for some odd prime p, then Op′(G)Z(J(S)) is a normal subgroup of G, for any Sylow p-subgroup S. J(S) is the Thompson subgroup of a p-group...

is just the group generated by u2. The socle is a characteristic subgroup, and hence a normal subgroup. It is not necessarily transitively normal, however...

international company operating in fashion and perfume sectors Puig subgroup, a characteristic subgroup in mathematical finite group theory Le Puy (disambiguation)...

core of C, the maximal normal subgroup of odd order). These are more or less the groups of Lie type of odd characteristic of large rank, and alternating...

Sylow theorems Hall subgroup Wreath product Butterfly lemma Center of a group Centralizer and normalizer Characteristic subgroup Commutator Composition...

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

group G, one can form the subgroup that consists of all its integer powers: ⟨g⟩ = { gk | k ∈ Z }, called the cyclic subgroup generated by g. The order...

its subgroups. This is also termed the Baer norm, after Reinhold Baer. The following facts are true for the Baer norm: It is a characteristic subgroup. It...

solvable group is a group whose derived series terminates in the trivial subgroup. Historically, the word "solvable" arose from Galois theory and the proof...

subgroup of G is normal in G, then G is called a T-group. Characteristic subgroup Normal core Normal closure Ascendant subgroup Descendant subgroup Serial...

is any of certain special normal subgroups of a group. The two most common types are the normal core of a subgroup and the p-core of a group. For a group...