publication . Preprint . Article . 2016

On loop extensions and cohomology of loops

Rolando Jimenez; Quitzeh Morales Meléndez;
Open Access English
  • Published: 07 Oct 2016
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.
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free text keywords: Mathematics - K-Theory and Homology, Mathematics - Rings and Algebras, Algebra and Number Theory, Mathematics, Correlation and dependence, Kernel (linear algebra), Commutative property, Quotient, Cohomology, Algebra

[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

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