On generating sets of finite algebras

• Autorzy: Krempa J. , Stocka A.

Identyfikatory

DOI

10.1515/dema-2015-0040

• Konferencja: Proceedings of the AAA88 - 88th Workshop on General Algebra Editors for the Special Issue: Anna Romanowska, Jonathan D. H. Smith
• Języki publikacji: EN

Abstrakty

EN

We consider here some notions and results about sets of generators of finite algebras motivated by the case of finite groups. We illustrate these notions by simple examples closed to lattices and semigroups. Next, we examine these notions in the case of groups with operators.

Słowa kluczowe

EN

finite algebra; join irreducible element; independence; Ω-group

PL

algebra skończona; niezależność; Ω-grupa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2015
• Tom: Vol. 48, nr 4
• Strony: 554--561
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Krempa J.

• Institute of Mathematics, University of Warsaw, Banacha 2, 02–097 Warszawa, Poland

autor

Stocka A.

• Institute of Mathematics, University of Białystok, Akademicka 2, 15–267 Białystok, Poland

Bibliografia

• [1] P. Apisa, B. Klopsch, A generalization of the Burnside basis theorem, J. Algebra 400 (2014), 8–16.
• [2] P. M. Cohn, Universal Algebra, Springer Netherlands, 1981.
• [3] A. L. Delgado, Yu-Fen Wu, On locally finite groups in which every element has prime power order, Illinois J. Math. 46(3) (2002), 885–891.
• [4] K. Głazek, General notion of independence, in: K. P. Shum, Z. X. Wan, J. P. Zhang (eds), Advances in Algebra, World Scientific, Singapore, 2003, pp. 112–128.
• [5] G. Grätzer, General Lattice Theory, (2nd edition), Birkhäuser Verlag, Basel, 1998.
• [6] L. Halbasen, M. Hamilton, P. Ruzicka, Minimal generating sets of groups, ring and filds, Quaestiones Math. 30(3) 2007, 355–363.
• [7] G. Higman, Finite groups in which every element has prime power order, J. London Math. Soc. 32 (1957), 335–342.
• [8] P. R. Jones, Basis properties for inverse semigroups, J. Algebra 50 (1978), 135–152.
• [9] J. Krempa, A. Stocka, On some invariants of finite groups, Int. J. Group Theory 2(1) (2013), 109–115.
• [10] J. Krempa, A. Stocka, On some sets of generators of finite groups, J. Algebra 405 (2014), 122–134.
• [11] J. Krempa, A. Stocka, Corrigendum to “On some sets of generators of finite groups”, J. Algebra 408 (2014), 61–62.
• [12] J. Krempa, A. Stocka, On finite groups with pp-basis property, Bull. Austral. Math. Soc. 91(2) (2015), 241–249.
• [13] E. Marczewski, Independence and homomorphisms in abstract algebras, Fund. Math. 50(1) (1961), 45–61.
• [14] J. McDougall-Bagnall, M. Quick, Groups with the basis property, J. Algebra 346 (2011), 332–339.
• [15] J. D. Mitchell, Y. Peresse, Sierpiński rank for groups and semigroups, Wiadom. Mat.48(2) (2012), 209–215.
• [16] J. J. Rotman, An Introduction to the Theory of Groups, Springer, 1994.
• [17] R. Scapellato, L. Verardi, Bases of certain finite groups, Ann. Math. Blaise Pascal 1 (1994), 85–93.
• [18] H. Whitney, On the abstract properties of linear dependence, Amer. J. Math. 57(3) (1935), 509–533.