publication . Preprint . Article . 2016

On loop extensions and cohomology of loops

Rolando Jimenez; Quitzeh Morales Meléndez;
Open Access English
  • Published: 07 Oct 2016
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.
Persistent Identifiers
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: 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:

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