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From these results, several groups of intermediates were identified.
Groups of intermediates with congruent structures, linked by the gray boxes in the figure, were observed to have nearly identical mobility, consistent with our expectations.
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Are there finitely generated simple groups of intermediate growth?
The m-АPAA molecule contains acidic groups of intermediate strength (−AsO3H2) and weakly basic groups (−NH2).
Are there finitely generated hereditary just-infinite groups of intermediate growth?
It is already known that there are finitely generated branch groups of intermediate growth.
A useful fact about groups of intermediate growth which we will use is due to Rosset [35].
The question on the existence of groups of intermediate growth was raised in 1968 by Milnor [30].
The class (mathcal{SG }backslash mathcal{EG }) contains the class of finitely generated groups of intermediate growth.
(v) Recall however that there exist groups of intermediate growth with uncountably many quotients: see [69] and Definition 4.13.
In fact, all known examples of groups of intermediate growth are of branch type or are reconstructions on the base of groups of branch type.
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