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Intermediately fully invariant subgroup

327 bytes added, 01:48, 14 August 2009
Metaproperties
An intermediately fully characteristic subgroup of an intermediately fully characteristic subgroup need not be intermediately fully characteristic. {{proofat|[[Intermediate full invariance is not transitive]]}}
{{join-closed|strongly}}
An arbitrary join of intermediately fully characteristic subgroups is intermediately fully characteristic. This follows from the fact that the intermediately operator preserves the property of being closed under joins.  {{proofat|[[Intermediate full invariance is strongly join-closed]]}}{{further|[[Intermediately operator preserves join-closedness]], [[Full invariance is strongly join-closed]]}} {{quot-transitive}}{{proofat|[[Intermediate full invariance is quotient-transitive]]}}{{further|[[Intermediately operator preserves quotient-transitivity]], [[Full invariance is quotient-transitive]]}}
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