AIM Loops and the AIM Conjecture

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21730%2F19%3A00346812" target="_blank" >RIV/68407700:21730/19:00346812 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.2478/forma-2019-0027" target="_blank" >https://doi.org/10.2478/forma-2019-0027</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.2478/forma-2019-0027" target="_blank" >10.2478/forma-2019-0027</a>

Result language

angličtina

Original language name

AIM Loops and the AIM Conjecture

Original language description

In this article, we prove, using the Mizar [2] formalism, a number of properties that correspond to the AIM Conjecture. In the first section, we define division operations on loops, inner mappings T, L and R, commutators and associators and basic attributes of interest. We also consider subloops and homomorphisms. Particular subloops are the nucleus and center of a loop and kernels of homomorphisms. Then in Section 2, we define a set Mlt Q of multiplicative mappings of Q and cosets (mostly following Albert 1943 for cosets [1]). Next, in Section 3 we define the notion of a normal subloop and construct quotients by normal subloops. In the last section we define the set InnAut of inner mappings of Q, define the notion of an AIM loop and relate this to the conditions on T, L, and R defined by satisfies TT, etc. We prove in Theorem (67) that the nucleus of an AIM loop is normal and finally in Theorem (68) that the AIM Conjecture follows from knowing every AIM loop satisfies aa1, aa2, aa3, Ka, aK1, aK2 and aK3.

Czech name

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Czech description

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Type

J_ost - Miscellaneous article in a specialist periodical

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

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Continuities

R - Projekt Ramcoveho programu EK

Publication year

2019

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Formalized Mathematics

ISSN

1426-2630

e-ISSN

1898-9934

Volume of the periodical

27

Issue of the periodical within the volume

4

Country of publishing house

PL - POLAND

Number of pages

15

Pages from-to

321-335

UT code for WoS article

000516828700001

EID of the result in the Scopus database

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