View source for Subgroup-cofactorial automorphism-invariant implies left-transitively 2-subnormal

{{subgroup property implication|
stronger = subgroup-cofactorial automorphism-invariant subgroup|
weaker = left-transitively 2-subnormal subgroup}}
{{composition computation|
left = subgroup-cofactorial automorphism-invariant subgroup|
right = 2-subnormal subgroup|
final = 2-subnormal subgroup}}

==Statement==

Suppose <math>H \le K \le G</math> are groups such that <math>H</math> is a [[subgroup-cofactorial automorphism-invariant subgroup]] of <math>K</math> and <math>K</math> is a [[2-subnormal subgroup]] of <math>G</math>. Then, <math>H</math> is also a 2-subnormal subgroup of <math>G</math>.