| 释义 |
- See also
- References
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 successor. The series may be infinite. If the series is finite, then the subgroup is subnormal. Here are some properties of ascendant subgroups: - Every subnormal subgroup is ascendant; every ascendant subgroup is serial.
- In a finite group, the properties of being ascendant and subnormal are equivalent.
- An arbitrary intersection of ascendant subgroups is ascendant.
- Given any subgroup, there is a minimal ascendant subgroup containing it.
See alsoReferences- {{cite book | title=Sylow Theory, Formations, and Fitting Classes in Locally Finite Groups | author=Martyn R. Dixon | publisher=World Scientific | year=1994 | isbn=981-02-1795-1 | page=6 }}
- {{cite book | title=A Course in the Theory of Groups | author=Derek J.S. Robinson | publisher=Springer-Verlag | year=1996 | isbn=0-387-94461-3 | page=358 }}
{{Abstract-algebra-stub}} 1 : Subgroup properties |