arXiv subjects

John Rhodes

Publications and source records attributed to John Rhodes.

40 records · Page 3Linked to original sources

arXiv2008

An Effective Lower Bound for Group Complexity of Finite Semigroups and Automata

The question of computing the group complexity of finite semigroups and automata was first posed in K. Krohn and J. Rhodes, \textit{Complexity of finite semigroups}, Annals of Mathematics (2) \textbf{88} (1968), 128--160, motivated by the Prime Decomposition Theorem of K. Krohn and J. Rhodes, \textit{Algebraic theory of machines, {I}: {P}rime decomposition theorem for finite semigroups and machines}, Transactions of the American Mathematical Society \textbf{116} (1965), 450--464. Here we provide an effective lower bound for group complexity.

math.GR↗

arXiv2007

Aperiodic Pointlikes and Beyond

We prove that if $π$ is a recursive set of primes, then pointlike sets are decidable for the pseudovariety of semigroups whose subgroups are $π$-groups. In particular, when $π$ is the empty set, we obtain Henckell's decidability of aperiodic pointlikes. Our proof, restricted to the case of aperiodic semigroups, is simpler than the original proof.

math.GR↗

arXiv2006

A Profinite Approach to Stable Pairs

We give a short proof, using profinite techniques, that idempotent pointlikes, stable pairs and triples are decidable for the pseudovariety of aperiodic monoids. Stable pairs are also described for the pseudovariety of all finite monoids.

math.GR↗

arXiv2006

Closed subgroups of free profinite monoids are projective profinite groups

We prove that the class of closed subgroups of free profinite monoids is precisely the class of projective profinite groups. In particular, the profinite groups associated to minimal symbolic dynamical systems by Almeida are projective. Our result answers a question raised by Lubotzky during the lecture of Almeida at the Fields Workshop on Profinite Groups and Applications, Carleton University, August 2005. We also prove that any finite subsemigroup of a free profinite monoid consists of idempotents.

math.GR↗