subnormal subgroup
1Subnormal 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… …
2Subgroup series — In mathematics, a subgroup series is a chain of subgroups: Subgroup series can simplify the study of a group to the study of simpler subgroups and their relations, and several subgroup series can be invariantly defined and are important… …
3Quasinormal subgroup — In mathematics, in the field of group theory, a quasinormal subgroup, or permutable subgroup, is a subgroup of a group that commutes (permutes) with every other subgroup. The term quasinormal subgroup was introduced by Oystein Ore in 1937.Two… …
4Conjugate-permutable subgroup — In mathematics, in the field of group theory, a conjugate permutable subgroup is a subgroup that commutes with all its conjugate subgroups. The term was introduced by Tuval Foguel in 1996 and arose in the context of the proof that for finite… …
5Ascendant subgroup — In mathematics, in the 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, such that every term in the series is a normal subgroup of its… …
6Normal subgroup — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …
7Pronormal subgroup — In mathematics, especially in the field of group theory, a pronormal subgroup is a subgroup that is embedded in a nice way. Pronormality is a simultaneous generalization of both normal subgroups and abnormal subgroups such as Sylow subgroups,… …
8Contranormal subgroup — In mathematics, in the field of group theory, a contranormal subgroup is a subgroup whose normal closure in the group is the whole group. Clearly, a contranormal subgroup can be normal only if it is the whole group. Some facts: Every subgroup of… …
9Fitting subgroup — In mathematics, especially in the area of algebra known as 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, it represents the smallest… …
10Descendant subgroup — In mathematics, in the 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, such that every term in the series is a normal subgroup of its… …
