Left residual of 2-subnormal by normal is normal of characteristic

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Template:Left residual computation

This article gives a proof/explanation of the equivalence of multiple definitions for the term normal subgroup of characteristic subgroup
View a complete list of pages giving proofs of equivalence of definitions

Statement

Suppose H is a subgroup of a group G. The following are equivalent:

  1. H is a Normal subgroup of characteristic subgroup (?) of G: in other words, there is a characteristic subgroup K of G such that H is a normal subgroup of K.
  2. Whenever G is a Normal subgroup (?) of some group L, H is a 2-subnormal subgroup (?) of L.

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