Cofactorial automorphism-invariant implies left-transitively 2-subnormal

From Groupprops
Jump to: navigation, search
This article gives the statement and possibly, proof, of an implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., cofactorial automorphism-invariant subgroup) must also satisfy the second subgroup property (i.e., left-transitively 2-subnormal subgroup)
View all subgroup property implications | View all subgroup property non-implications
Get more facts about cofactorial automorphism-invariant subgroup|Get more facts about left-transitively 2-subnormal subgroup
This article describes a computation relating the result of the Composition operator (?) on two known subgroup properties (i.e., Cofactorial automorphism-invariant subgroup (?) and 2-subnormal subgroup (?)), to another known subgroup property (i.e., 2-subnormal subgroup (?))
View a complete list of composition computations


Suppose H \le K \le G are groups such that H is a cofactorial automorphism-invariant subgroup of K and K is a 2-subnormal subgroup of G. Then, H is a 2-subnormal subgroup of G.

Related facts

Facts used

  1. Subgroup-cofactorial automorphism-invariant implies left-transitively 2-subnormal


The proof follows from Fact (1).