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...

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...

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

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

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

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

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...

{\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...

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

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...

normal subgroup, Z ( G ) ◃ G {\displaystyle Z(G)\triangleleft G} , and also a characteristic subgroup, but is not necessarily fully characteristic. The...

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...

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...

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

properties Both Ωi(G) and ℧i(G) are characteristic subgroups of G for all natural numbers, i. The omega and agemo subgroups form two normal series: G = ℧0(G)...

subgroups are the only fully characteristic subgroups of a free group and therefore represent the generic example of fully characteristic subgroups,...

(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...

mathematics, 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)...

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...

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

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...

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...

{Inn} (G)} is the group of inner automorphisms of G.) K ≤ G is a characteristic subgroup if and only if λ(K) ⊴ Hol(G) Hall, Marshall Jr. (1959), The theory...

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

G\mid gs=sg{\text{ for all }}s\in S\}.} characteristic subgroup A subgroup of a group is a characteristic subgroup of that group if it is mapped to itself...

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

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

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...

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...

In mathematics, a characteristic class is a way of associating to each principal bundle of X a cohomology class of X. The cohomology class measures the...