publication . Article . Preprint . 2016

On loop extensions satisfying one single identity and cohomology of loops

Benítez, Rolando Jiménez; Meléndez, Quitzeh Morales;
Restricted
  • Published: 07 Oct 2016 Journal: Communications in Algebra, volume 45, pages 3,667-3,690 (issn: 0092-7872, eissn: 1532-4125, Copyright policy)
  • Publisher: Informa UK Limited
Abstract
In this paper are defined cohomology-like groups that classify loop extensions satisfying a given identity in three variables for association identities, and in two variables for the case of commutativity. It is considered a large amount of identities. This groups generalize those defined in works of Nishigori [2] and of Jhonson and Leedham-Green [4]. It is computed the number of metacyclic extensions for trivial action of the quotient on the kernel in one particular case for left Bol loops and in general for commutative loops.
Subjects
free text keywords: Topology, Kernel (linear algebra), Cohomology, Quotient, Mathematics, Commutative property, Algebra, Mathematics - K-Theory and Homology, Mathematics - Rings and Algebras

[1] Eilenberg S., Maclane S., Cohomology theory in abstract groups I Ann. of math. Vol. 48, No. 1 (1947), 51-78.

[2] Nishigori N., On Loop Extensions of Groups and M-cohomology Groups I. J. Sci. HIROSHIMA UNIV. SER. A-I 27 (1963), 151-165.

[3] Nishigori N., On Loop Extensions of Groups and M-cohomology Groups II. J. Sci. HIROSHIMA UNIV. SER. A-I 29 (1965), 17-26. [OpenAIRE]

[4] Kenneth W.J., Ch.R. Leedham-Green Loop cohomology Czec. Math. J., Vol. 40 (1990), No. 2, 182-194.

[5] P.T. Nagy; K. Strambach Schreier loops Czec. Math. J., Vol. 58 (2008), No. 3, 759-786. Instituto de Matema´ticas, Representacio´n Oaxaca, Universidad Nacional Auto´noma de M´exico, Leo´n 2, 68000 Oaxaca de Jua´rez, Oaxaca, M´exico E-mail address: rolando@matcuer.unam.mx Universidad Pedago´gica Nacional, unidad 201 Camino a la Zanjita S/N, Col. Noche Buena, Santa Cruz Xoxocotla´n, Oaxaca. C.P. 71230 E-mail address: qmoralesme@conacyt.mx [OpenAIRE]

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publication . Article . Preprint . 2016

On loop extensions satisfying one single identity and cohomology of loops

Benítez, Rolando Jiménez; Meléndez, Quitzeh Morales;