Dualizability of automatic algebras

Bentz, Wolfram; Davey, Brian A.; Pitkethly, Jane G.; Willard, Ross

doi:10.1016/j.jpaa.2013.11.020

Cited by 3 publications

(2 citation statements)

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“…Theorem 5.2 implies Theorem 2.5 of [3] (a fact that is alluded to in Remark 2.6 of [3]). Conversely, it appears that some cases where we apply Theorem 3.1 can alternatively be obtained using embellishments of the constructions in the proof of [3, Theorem 2.5], though not when, for example, a = c.…”

Section: Nilpotent and Monogenic Semigroupsmentioning

confidence: 82%

“…This gives an interpretation of T, and the remainder of the argument is essentially a simplified version of the final stages of the application of Theorem 3.1 in the proof of Theorem 5.1. Theorem 5.2 implies Theorem 2.5 of [3] (a fact that is alluded to in Remark 2.6 of [3]). Conversely, it appears that some cases where we apply Theorem 3.1 can alternatively be obtained using embellishments of the constructions in the proof of [3, Theorem 2.5], though not when, for example, a = c.…”

Section: Nilpotent and Monogenic Semigroupsmentioning

confidence: 82%

See 1 more Smart Citation

Natural dualities, nilpotence and projective planes

Jackson

2015

Algebra Univers.

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We use an interpretation of projective planes to show the inherent nondualisability of some finite semigroups. The method is sufficiently flexible to demonstrate the nondualisability of (asymptotically) almost all finite semigroups as well as to give a fresh proof of the Quackenbush-Szabó result that any finite group with a nonabelian Sylow subgroup is nondualisable. A novel feature is that the ostensibly different notions of nilpotence for semigroups, nilpotence for groups, and the property of being nonorthodox for a completely 0-simple semigroup are unified by way of a single construction. We also give a semigroup example of two dualisable finite semigroups whose direct product is inherently nondualisable.2000 Mathematics Subject Classification. Primary: 08C20. Secondary: 20M07, 20M17.

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Section: Nilpotent and Monogenic Semigroupsmentioning

confidence: 82%

Section: Nilpotent and Monogenic Semigroupsmentioning

confidence: 82%