Complexity Pseudovarieties Are not Local: Type Ii Subsemigroups Can Fall Arbitrarily in Complexity


We prove the following two results announced by Rhodes: The Type II subsemigroup of a finite semigroup can fall arbitrarily in complexity; the complexity pseudovarieties Cn (n ≥ 1) are not local. 
DOI: 10.1142/S0218196706003177


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