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{{arbitrarily large subnormal depth statement}}
 
==Statement==
with each <math>H_i</math> normal in <math>H_{i+1}</math>, and there exists ''no'' series of length <math>k-1</math> with the property.
 
==Related facts==
 
* [[Stronger than::Normality is not transitive]]
* [[Weaker than::Descendant not implies subnormal]], [[Weaker than::there exist subgroups of arbitrarily large descendant depth]]
* [[Weaker than::Ascendant not implies subnormal]], [[Weaker than::there exist subgroups of arbitrarily large ascendant depth]]
* [[Weaker than::Normal not implies left-transitively fixed-depth subnormal]]
* [[Weaker than::Normal not implies right-transitively fixed-depth subnormal]]
==Proof==
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