Groupprops, The Group Properties Wiki (pre-alpha)
Take a short survey about Math Resources on the Internet.
Automorph-join-closed subnormal of normal implies conjugate-join-closed subnormal
From Groupprops
This article describes a computation relating the result of the composition operator on two known subgroup properties (i.e., automorph-join-closed subnormal subgroup and normal subgroup), to another known subgroup property (i.e., conjugate-join-closed subnormal subgroup)
View a complete list of composition computations
Contents |
Statement
Statement with symbols
If H is an automorph-join-closed subnormal subgroup of K and K is a normal subgroup of G, then H is a conjugate-join-closed subnormal subgroup of G.
Related facts
- Left residual of conjugate-join-closed subnormal by normal equals automorph-join-closed subnormal
- Finite-automorph-join-closed subnormal of normal implies finite-conjugate-join-closed subnormal
- Join-transitively subnormal of normal implies finite-conjugate-join-closed subnormal
- 3-subnormal implies finite-conjugate-join-closed subnormal
Proof
Fill this in later
