I-automorphism-invariance satisfies intermediate subalgebra condition
From Groupprops
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Statement
Suppose 
is a variety of algebras, A is an algebra of and B is a subalgebra of A such that for every I-automorphism 
of A, 
. Then, if C is a subalgebra of A containing B, every I-automorphism of C also sends B to itself.
Related facts
Particular cases
- Normality satisfies intermediate subgroup condition: For the variety of groups, the I-automorphisms are the inner automorphisms, and the subgroups invariant under these automorphisms are the normal subgroups. Thus, the statement translates to saying that a normal subgroup of a group is normal in every intermediate subgroup.
