subnormal group

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• Subnormal subgroup — In mathematics, in the field of group theory, a subgroup H of a given group G is a subnormal subgroup of G if there is a chain of subgroups of the group, each one normal in the next, beginning at H and ending at G .In notation, H is k subnormal… …   Wikipedia

• Core (group) — In group theory, a branch of mathematics, a core 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. Contents 1 The normal core 1.1 Definition 1.2… …   Wikipedia

• HN group — In mathematics, in the field of group theory, a HN group or hypernormalizing group is a group with the property that the hypernormalizer of any subnormal subgroup is the whole group.For finite groups, this is equivalent to the condition that the… …   Wikipedia

• Quasisimple group — In mathematics, a quasisimple group (also known as a covering group) is a group that is a perfect central extension E of a simple group S . In other words, there is a short exact sequence:1 rarr; Z ( E ) rarr; E rarr; S rarr; 1such that E = [ E …   Wikipedia

• T-group (mathematics) — In mathematics, in the field of group theory, a T group is a group in which the property of normality is transitive, that is, every subnormal subgroup is normal. Here are some facts about T groups:*Every abelian group and every Hamiltonian group… …   Wikipedia

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

• Polycyclic group — In mathematics, especially in the area of abstract algebra known as group theory, a polycyclic group is a solvable group that satisfies the maximal condition on subgroups (that is, every subgroup is finitely generated).Equivalently, a group G is… …   Wikipedia

• Imperfect group — In mathematics, in the area of algebra known as group theory, an imperfect group is a group with no nontrivial perfect quotients. Some of their basic properties were established in harv|Berrick|Robinson|1993. The study of imperfect groups… …   Wikipedia

• Iwasawa group — In mathematics a group is sometimes called an Iwasawa group or M group or modular group if its lattice of subgroups is modular.Finite modular groups are also called Iwasawa groups, after harv|Iwasawa|1941 where they were classified. Both finite… …   Wikipedia

• Component (group theory) — In mathematics, in the field of group theory, a component of a finite group is a quasisimple subnormal subgroup. Any two distinct components commute. The product of all the components is the layer of the group. For finite abelian (or nilpotent)… …   Wikipedia

• Stability group — In mathematics, in the realm of group theory, stability group of subnormal series is the group of automorphisms that act as identity on each quotient group …   Wikipedia