Groupprops, The Group Properties Wiki (pre-alpha)
Take a short survey about Math Resources on the Internet.
Group in which every proper subgroup is contained in a maximal subgroup
From Groupprops
(Redirected from Group in which every subgroup is contained in a maximal subgroup)
This article defines a group property: a property that can be evaluated to true/false for any given group
View a complete list of group properties
VIEW RELATED:
RANDOM GROUP PROPERTY: Noetherian group: A group where every subgroup is finitely generated.
This is a variation of finiteness (groups)
Find other variations of finiteness (groups) |
Contents |
Definition
Symbol-free definition
A group in which every proper subgroup is contained in a maximal subgroup is a group for which every proper subgroup (subgroup that is not the whole group) is contained in a maximal subgroup (a proper subgroup not contained in any other proper subgroup).
Relation with other properties
Stronger properties
Facts
For such a group, the Frattini subgroup is indeed the largest Frattini-embedded normal subgroup.
