Author:
Marín Víctor, ,Pinedo Héctor,
Abstract
We present some constructions of groupoids such as: direct product, semidirect product and give necessary and sufficient conditions for a groupoid to be embedded into a direct product of groupoids. Also, we establish necessary and sufficient conditions to determine when a semidirect product is direct. Finally the notion of solvable groupoid is introduced and studied, in particular it is shown that a finite groupoid G is solvable if and only if its isotropy groups are.
Publisher
Luhansk Taras Shevchenko National University
Subject
Discrete Mathematics and Combinatorics,Algebra and Number Theory
Reference19 articles.
1. [1]F. Abadie, Partial actions and groupoids,Proc. Am. Math. Soc,132(2004) 1037-1047.
2. [2]M. Akhavan-Malayeri, On Solvable Groups of Arbitrary Derived Length and SmallCommutator Length,Int. J. Math. Math. Sci.2011, Article ID 245324, 5 pages.
3. [3]J. Ávila, V. Marín, The Notions of Center, Commutator and Inner Isomorphismfor Groupoids,Ingeniería y Ciencia,16(2020) 7-26.
4. [4]J. Ávila, V. Marín and H. Pinedo, Isomorphism Theorems for Groupoids and SomeApplications,Int. J. Math. Math. Sci.2020(2020) 1-10.
5. [5]G. Beier, C. Garcia, W. Lautenschlaeger and T. Tamusiunas, Generalizations ofLagrange and Sylow Theorems for Groupoids,preprint.