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João Araújo

Institutional Address

Universidade Aberta
Departamento de Matemática
Rua da Escola Politécnica, 147
1269-001 LISBOA

Phone: | Email:


Associate Professor with Habilitation, Universidade Aberta


Algebra and Computing

Principal Area

Semigroups, groups, combinatorics and and computational algebra


  • Habilitation in Mathematics, University of Lisbon, 2011.
  • PhD in mathematics, University of York, UK, 2000, KM Stott Memorial Prize.
  • MSc in Mathematics, University of Lisbon, 1994.
  • Degree in mathematics, University of Lisbon, 1991.


Papers in International Journals

Araújo, João; Kinyon, M.; Vigário, Edgar (2019) Short equational bases for MV-Algebras, commutative BCK-Algebras and LBCK-algebras. (submitted).
Araújo, João; Cameron, P. J. (2019) Primitive groups, road closures, and idempotent generation . (submitted).
Araújo, João; Kinyon, M.; R. Padmanabhan (2019) A 2-base for inverse semigroups. (submitted).
Araújo, João; Kinyon, M. (2019) Decidability and Independence of Conjugacy Problems in Finitely Presented Monoids . (submitted).
Araújo, João; Bentz, Wolfram; Cameron, P. J. (2018) Orbits of Primitive k-Homogenous Groups on (n-k)-Partitions with Applications to Semigroups . Transactions of the American Mathematical Society.
Araújo, João; Bentz, Wolfram; Janusz Konieczny; Joy Morris (2017) Automorphism Groups of Circulant Digraphs with Applications to Semigroup Theory. Combinatorica, 1-28.
Araújo, João; Bentz, Wolfram; Janusz Konieczny (2017) Directed graphs of inner translations of semigroups. Semigroup Forum: 94(3), 650-673.
Araújo, João; Cameron, P. J.; Hulpke, A.; Lopes,P. (2017) Imprimitive Permutations in Primitive Groups . Journal of Algebra: 486, 396-416.
Araújo, João; Janusz Konieczny; António Malheiro (2017) Four Notions of Conjugacy for Abstract Semigroups . Proceedings of the Royal Academy of the Edinbourgh Mathematical Society: 147 A, 1169-1214.
Araújo, João; Gomes, Gracinda M. S.; Bentz, Wolfram (2017) Congruences on direct products of transformation and matrix monoids. Proceedings of the Royal Academy of the Edinbourgh Mathematical Society: 147 A, 1169-1214.
Araújo, João; Peter J Cameron; Benjamin Steinberg (2017) Between primitive and $2$-transitive: Synchronization and its friends . European Mathematical Society Surveys: 4:2, 101-184.
Araújo, João; Cameron, Peter (2016) Two Generalizations of Homogeneity in Groups with Applications to Regular Semigroups . Trans. Amer. Math. Soc.: 368, 1159--1188.
André, Jorge M.; Araújo, João; Cameron, Peter (2016) The classification of partition homogeneous groups with applications to semigroup theory. Journal of Algebra: 452, 288--310.
Araújo, João; Bentz, Wolfram; Cameron, P. J.; Gordon Royle; Artur Schaefer (2016) Primitive Groups, Graph Endomorphisms and Synchronization. Proceedings of the London Mathematical Society: 113, 829--867.
Araújo, João; Kinyon, M. (2015) A natural characterization of semilattices of rectangular bands and groups of exponent two. Semigroup Forum: 91, 295-298.
Araújo, João; Bentz, Wolfram; Mitchell, James D.; Schneider, Csaba (2015) The rank of the semigroup of transformations stabilising a partition of a finite set.  Math. Proc. Cambridge Philos. Soc.: 159, 339-353.
Araújo, João; Janusz Konieczny; Malheiro, António (2014) Conjugation in semigroups. Journal of Algebra: 403, 93-134.
Araújo, João; Bentz, Wolfram; Konieczny, Janusz (2014) The largest subsemilattices of the endomorphism monoid of an independence algebra. Linear Algebra and its Applications: 458, 50-79.
Araújo, João; Cameron, Peter (2014) Primitive Groups Synchronize Non-uniform Maps of Extreme Ranks. Journal of Combinatorial Theorie, Series B: 106, 98-114.
Araújo, João; Kinyon, M. (2014) Inverse semigroups with idempotent-fixing automorphisms. Semigroup Forum: 89(2), 469-474.
Araújo, João; Bentz, Wolfram; Janusz Konieczny (2014) The Commuting Graph of the Symmetric Inverse Semigroup. Israel Journal of Mathematics: 207, 103-149.
Araújo, João; Konieczny, Janusz (2013) Centralizers in the Full Transformation Semigroup. Semigroup forum: 86(1), 1-31.
Araújo, João; Bentz, Wolfram; Cameron, Peter (2013) Groups synchronizing a transformation of non-uniform kernel. Theoretical Computer Science: 498, 1--9.
Araújo, João; Cameron, Peter; Mitchell, James D.; Neunhöffer, Max  (2013) The classification of normalizing groups. Journal of Algebra: 373, 481-490.
Araújo, João; Kinyon, M.; Malheiro, António (2013) A characterization of adequate semigroups by forbidden subsemigroups. Proceedings of the Royal Society of Edinburgh Series A: 143(6), 1115-1122.
Araújo, João; Konieczny, Janusz (2012) A Method for Finding New Sets of Axioms for Classes of Semigroups. Archives for Mathematical Logic: 51(5-6), 461-474.
Araújo, João; Kinyon, M. (2012) Axioms for Unary Semigroups Via Division Operations. Communications in Algebra: 40(2), 719-737.
Araújo, João; Kinyon, M. (2012) On a Problem of M. Kambites Regarding Abundant Semigroups . Communications in Algebra: 40(12), 4439–4447.
Araújo, João; Kinyon, M. (2011) An Elegant 3-Basis for Inverse Semigroups. Semigroup Forum: 82(2), 319-323.
Araújo, João; Fernandes, Vítor Hugo; Jesus, Manuel M.; Maltcev, Victor; Mitchell, James D. (2011) Automorphisms of partial endomorphism semigroups. Publicationes Mathematicae Debrecen: 79(1-2), 23-29.
André, Jorge M.; Araújo, João; Konieczny, J. (2011) Regular centralizers of idempotent transformations. Semigroup Forum: 82(2), 307-318.
Araújo, João; Edmundo, M.; Givant, S. (2011) v*-algebras, Independence Algebras and Logic. International Journal on Algebra and Computation: 21, 7, 1237-1257.
Araújo, João; Kinyon, M. (2011) Independent axiom systems for nearlattices. Czechoslovak Mathematical Journal: 61(4), 975-992.
Araújo, João; Mitchell, James D.; Schneider, Csaba (2011) Groups that together with any transformation generate regular semigroups or idempotent generated semigroups. Journal of Algebra: 343(1), 93-106.
Araújo, João; Kinyon, M.; Konieczny, J. (2011) Minimal Paths in the Commuting Graphs of Semigroups . European Journal of Combinatorics: 32, 178-197.
Araújo, João; Malheiro, António (2011) On finite complete presentations and exact decompositions of semigroups. Communications in Algebra: 39, 10, 3866--3878.
Araújo, João; McCune, William (2010) Computer Solutions of Problems in Inverse Semigroups. Communications in Algebra: 38(3), 1104-1121.
Araújo, João; Bunau, P. V.; Mitchell, James D.; Neunhoeffer, M. (2010) Computing Automorphisms of Semigroups. Journal of Symbolic Computation: 45(3), 373-392.
Araújo, João; Dobson, Edward; Konieczny, Janusz (2010) Automorphisms of Endomorphism Semigroups of Reflexive Digraphs. Mathematische Nachrichten: 283(7), 1-26.
Araújo, João; Konieczny, Janusz (2009) Automorphisms of Endomorphism Monoids of 1-Simple Free Algebras. Communications in Algebra: 37(1), 83-94.
Araújo, João; Schneider, Csaba (2009) The Rank of the Endomorphism Monoid of a Uniform Partition. Semigroup Froum: 78(3), 498-510.
Araújo, João; Konieczny, Janusz (2009) General Theorems on Automorphisms of Semigroups and Their Applications. Journal of the Australian Mathematical Society: 87(1), 1-17.
Araújo, João; Wehrung, Friedrich (2009) Embedding properties of endomorphism semigroups. Fundamenta Mathematicae: 202, 125-146.
Araújo, João; Konieczny, Janusz (2007) A Method of Finding Automorphism Groups of Endomorphism Monoids of Relational Systems. Discrete Mathematics: 307, 1609-1620.
Araújo, João; Konieczny, Janusz (2007) Automorphisms of Endomorphism Monoids of Relatively Free Bands. Proceedings of the Edinburgh Mathematical Society: 50, 1-21.
Araújo, João; Mitchell, James D. (2007) Relative ranks in the monoid of endomorphisms of an independence algebra. Monatshefte für Mathematik: 151, 1-10.
Araújo, João (2006) Lifts for Semigroups of Endomorphisms of an Independence Algebra. Colloquium Mathematicum: 106, 39-56.
Araújo, João; Fountain, John (2005) A Description of Normal Semigroups of Endomorphisms of Proper Independence Algebras. Communications in Algebra: 33, 2705-2711.
Araújo, João; Konieczny, Janusz (2005) Dense Relations Are Determined by Their Endomorphism Monoid. Semigroup Forum: 70, 2, 302-306.
Araújo, João; Mitchell, James D. (2005) An elementary proof that every singular matrix is a product of idempotent matrices. American Mathematical Monthly: 112 (7), 641-645.
Araújo, João; Silva, Fernando C. (2005) Semigroups of Matrices Closed Under Conjugation by Normal Linear Groups. JP Journal of Algebra and Number Theory: 5 No.3, 535-545.
Araújo, João; Konieczny, Janusz (2004) Semigroups of Transformations Preserving an Equivalence Relation and a Cross-Section. Communications in Algebra: 32, 1917-1935.
Araújo, João; Mitchell, James D.; Silva, N. (2003) On embedding countable sets of endomorphisms. Algebra Universalis: 50, 61-67.
Araújo, João (2003) Idempotent Generated Endomorphisms of an Independence Algebra. Semigroup Forum: 67, 464-467.
Araújo, João; Konieczny, Janusz (2003) Automorphisms Groups of Centralizers of Idempotents. Journal of Algebra: 269, 227-239.
Araújo, João (2003) Lifts for Semigroups of Monomorphisms of an Independence Algebra. Colloquium Mathematicum: 97, 277-284.
Araújo, João; Konieczny, Janusz (2002) Molaei's Generalized Groups are Completely Simple Semigroups. Bul. Inst. Politeh. Jassy, Sect. I. Mat. Mec. Teor. Fiz.: 48 (52) no. 1-2, 1-5.
Araújo, João (2002) On Idempotent Generated Semigroups. Semigroup Forum: 65, 138-140.
Araújo, João (2002) Generators for the Semigroup of Endomorphisms of an Independence Algebra. Algebra Colloquium: 9:4, 375-382.
Araújo, João (2002) Normal Semigroups of Endomorphisms of Proper Independence Algebras are Idempotent Generated. Proc. Edinburgh Math. Soc.: 45, 205-217.
Araújo, João; Silva, F. C. (2000) Semigroups of linear endomorphisms closed under conjugation. Comm. Algebra: 28 (8), 3679-3689.
Araújo, João; Bentz, Wolfram; Gomes, Gracinda M. S. () Congruences on Direct Products of Transformation and Matrix Monoids .  Semigroup Forum: (submitted).

Papers or Chapters in Edited Books

Araújo, João; Cameron, Peter (2015) Permutation groups and transformation semigroups: results and problems . London Mathematical Society Lecture Note Series: 422, 128-141.
Araújo, João; Konieczny, Janusz (2008) The Monoid of Holomorphic Endomorphisms of a Group and its Automorphisms. Semigroups, Acts and Categories with Applications to Graphs, Estonian Mathematical Society , 7-13.
Araújo, João; Fountain, John (2004) The Origins of Independence Algebras. Proceedings of the Workshop on Semigroups and Languages (Lisbon 2002), World Scientific, 54-67.


Araújo, João (2000) Aspects of the endomorphism monoids of independence algebras. K M Stott Memorial Prize Award Winning Ph.D. Thesis, University of York, United Kingdom.
Araújo, João (1994) Mergulhos e Coberturas de Semigrupos E-unitários, Dissertação de Mestrado em Matemática. Universidade de Lisboa.


The Mathematician as a Manager (2013-05-10) Instituto para a Investigação Interdisciplinar da Universidade de Lisboa
Semigroups of Transformations and the classification of finite simple groups (2007-02-27) Centro de Matemática da Universidade de Coimbra
Semigroups of Transformations and the Classification of Finite Simple Groups (2007-02-27) Centro de Matemática da Universidade de Coimbra, Portugal
Tudo o que Sempre quis Saber sobre Semigrupos (e não sabia como perguntar) (2006-11-08) Universidade Aberta, Lisboa, Portugal
A John Fountain Production: João Araújo in Tales in Semigroup Theory (2006-10-13) Fountainfest "Semigroups, categories and automata", a conference celebrating John Fountain's 65th birthday and his mathematical achievements, University of York, UK
O Coelho da Cartola (2006-10-02) CELC, Lisboa, Portugal
The Gold Rush (2006-06-22) Encontro Nacional da Sociedade Portuguesa de Matemática 2006, Instituto Superior de Engenharia de Lisboa (ISEL), Portugal
Álgebras de Independência: Um Serviço de Estrangeiros e Fronteiras entre a Álgebra Linear e os Semigrupos (2004-05-17) Centre de Estruturas Lineares e Combinatórias, Universidade de Lisboa
Semigrupos que Preservam Relações de Aridade Arbitrária (2004-05-13) Universidade de Évora
Do Vitor à Victória (2003-10-17)
Independence Algebras (2002-11-27) Workshop on Semigroups and Languages, CAUL, Portugal
Semigrupos normais de endomorfismos de uma álgebra de independência (2001-10-12)
Automorfismos de Semigrupos (2000-05-19)


Conference on Semigroups, Acts and Categories with Applications to Graphs University of Tartu, Estonia, 27-30/06/2007  (Contributed Talk)
Workshop Estatística, Matemática e Computação Universidade Aberta, Lisboa, Portugal, 8-9/11/2006  (Invited Speaker)
Fountainfest "Semigroups, categories and automata", a conference celebrating John Fountain's 65th birthday and his mathematical achievements University of York, UK, 12-14/10/2006  (Invited Speaker)
Computational and algorithmic aspects of semigroup theory - An international workshop St. Andrews, Scotland, 5-9/09/2006  (Invited Speaker)
Encontro Nacional da Sociedade Portuguesa de Matemática 2006 Instituto Superior de Engenharia de Lisboa (ISEL), Portugal, 20-23/06/2006  (Invited Speaker)
International Workshop on Semigroups and Languages CAUL, Lisbon, Portugal, 27-29/11/2002  (Contributed Talk)