Steiner loops satisfying the statement of Moufang's theorem

Maria De Lourdes Merlini Giuliani; Giliard Souza Dos Anjos; Charles Colbourn

Steiner loops satisfying the statement of Moufang's theorem

Maria De Lourdes Merlini Giuliani, Giliard Souza Dos Anjos, Charles Colbourn

Research output: Contribution to journal › Article › peer-review

Abstract

Andrew Rajah posed at the Loops'11 Conference in Trest, Czech Republic, the following conjecture: Is every variety of loops that satisfies Moufang's theorem contained in the variety of Moufang loops? This paper is motivated by that problem. We give a partial answer to this question and present two types of Steiner loops, one that satisfies Moufang's theorem and another that does not, and neither is Moufang loop.

Original language	English (US)
Pages (from-to)	103-108
Number of pages	6
Journal	Quasigroups and Related Systems
Volume	24
Issue number	1
State	Published - 2016

Keywords

Moufang loop
Moufang theorem
Steiner loop

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics

Cite this

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title = "Steiner loops satisfying the statement of Moufang's theorem",

abstract = "Andrew Rajah posed at the Loops'11 Conference in Trest, Czech Republic, the following conjecture: Is every variety of loops that satisfies Moufang's theorem contained in the variety of Moufang loops? This paper is motivated by that problem. We give a partial answer to this question and present two types of Steiner loops, one that satisfies Moufang's theorem and another that does not, and neither is Moufang loop.",

keywords = "Moufang loop, Moufang theorem, Steiner loop",

author = "{De Lourdes Merlini Giuliani}, Maria and {Dos Anjos}, {Giliard Souza} and Charles Colbourn",

note = "Funding Information: The second author was partially supported by FAPESP, Proc. 2012/21323-0",

year = "2016",

language = "English (US)",

volume = "24",

pages = "103--108",

journal = "Quasigroups and Related Systems",

issn = "1561-2848",

publisher = "Institute of Mathematics at the Academy of Sciences of Moldova",

number = "1",

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T1 - Steiner loops satisfying the statement of Moufang's theorem

AU - De Lourdes Merlini Giuliani, Maria

AU - Dos Anjos, Giliard Souza

AU - Colbourn, Charles

N1 - Funding Information: The second author was partially supported by FAPESP, Proc. 2012/21323-0

PY - 2016

Y1 - 2016

N2 - Andrew Rajah posed at the Loops'11 Conference in Trest, Czech Republic, the following conjecture: Is every variety of loops that satisfies Moufang's theorem contained in the variety of Moufang loops? This paper is motivated by that problem. We give a partial answer to this question and present two types of Steiner loops, one that satisfies Moufang's theorem and another that does not, and neither is Moufang loop.

AB - Andrew Rajah posed at the Loops'11 Conference in Trest, Czech Republic, the following conjecture: Is every variety of loops that satisfies Moufang's theorem contained in the variety of Moufang loops? This paper is motivated by that problem. We give a partial answer to this question and present two types of Steiner loops, one that satisfies Moufang's theorem and another that does not, and neither is Moufang loop.

KW - Moufang loop

KW - Moufang theorem

KW - Steiner loop

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M3 - Article

AN - SCOPUS:84983371839

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VL - 24

SP - 103

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JO - Quasigroups and Related Systems

JF - Quasigroups and Related Systems

IS - 1

ER -

Steiner loops satisfying the statement of Moufang's theorem

Abstract

Keywords

ASJC Scopus subject areas

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