fully normal subgroup

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• Fully normalized subgroup — In mathematics, in the field of group theory, a subgroup of a group is said to be fully normalized if every automorphism of the subgroup lifts to an inner automorphism of the whole group. Another way of putting this is that the natural embedding… …   Wikipedia

• Normal subgroup — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia

• Characteristic subgroup — In mathematics, particularly in the area of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is invariant under all automorphisms of the parent group.[1][2] Because conjugation is an automorphism, every… …   Wikipedia

• Commutator subgroup — In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.[1][2] The commutator subgroup is important because it is the smallest… …   Wikipedia

• Quotient group — In mathematics, given a group G and a normal subgroup N of G , the quotient group, or factor group, of G over N is intuitively a group that collapses the normal subgroup N to the identity element. The quotient group is written G / N and is… …   Wikipedia

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• Point groups in three dimensions — In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O(3), the group of all isometries… …   Wikipedia

• Charakteristische Untergruppe — In der Gruppentheorie ist eine charakteristische Untergruppe einer Gruppe G eine Untergruppe H, die unter jedem Automorphismus von G fest bleibt. Das heißt, eine Untergruppe H von G heißt charakteristisch, wenn für jeden Automorphismus… …   Deutsch Wikipedia

• Center (group theory) — In abstract algebra, the center of a group G is the set Z ( G ) of all elements in G which commute with all the elements of G . That is,:Z(G) = {z in G | gz = zg ;forall,g in G}.Note that Z ( G ) is a subgroup of G , because # Z ( G ) contains e …   Wikipedia

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