Shortest single axioms with neutral element
for groups of exponent 2 and 3

Fiala NickC.; Agre Keith

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Articolul urmator

817

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2022-06-07 20:00

SM ISO690:2012

FIALA, NickC., AGRE, Keith. Shortest single axioms with neutral element for groups of exponent 2 and 3. In: Quasigroups and Related Systems, 2013, vol. 21, nr. 1(29), pp. 69-82. ISSN 1561-2848.

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Quasigroups and Related Systems

Volumul 21, Numărul 1(29) / 2013 / ISSN 1561-2848

Shortest single axioms with neutral element for groups of exponent 2 and 3

Pag. 69-82

Fiala NickC., Agre Keith

St. Cloud State University

Disponibil în IBN: 30 octombrie 2014

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Rezumat

In this note, we study identities in product and a constant e only that are valid in all groups of exponent 2 (3) with neutral elemente and that imply that a groupoid satisfying one of them is a group of exponent 2 (3) with neutral element e. Such an identity will be called a single axiom with neutral element for groups of exponent 2 (3). We utilize the automated reasoning software Prover9 and Mace4 to attempt to nd all shortest single axioms with neutral element for groups of exponent 2 (3). Beginning with a list of 1323 (1716) candidate identities that contains all shortest possible single axioms with neutral element for groups of exponent 2 (3), we nd 173 (148) single axioms with neutral element for groups of exponent (2) 3 and eliminate all but 5 (119) of the remaining identities as not being single axioms with neutral element for groups of exponent 3. We also prove that a nite model of any of these 5 (119) identities must be a group of exponent 2 (3) with neutral elemente

Cuvinte-cheie
Group,

neutral element, exponent, single axiom, automated reasoning

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<dc:creator>Fiala, N.</dc:creator>
<dc:creator>Agre, K.M.</dc:creator>
<dc:date>2013-02-01</dc:date>
<dc:description xml:lang='en'>In this note, we study identities in product and a constant e only that are valid in all groups of exponent 2 (3) with neutral elemente and that imply that a groupoid satisfying one of them is a group of exponent 2 (3) with neutral element e. Such an identity will be called a single axiom with neutral element for groups of exponent 2 (3). We utilize the automated reasoning
software Prover9 and Mace4 to attempt to nd all shortest single axioms with neutral element for groups of exponent 2 (3). Beginning with a list of 1323 (1716) candidate identities that contains all shortest possible single axioms with neutral element for groups of exponent 2 (3), we nd 173 (148) single axioms with neutral element for groups of exponent (2) 3 and eliminate all but 5 (119) of the remaining identities as not being single axioms with neutral element for groups of
exponent 3. We also prove that a nite model of any of these 5 (119) identities must be a group of exponent 2 (3) with neutral elemente</dc:description>
<dc:source>Quasigroups and Related Systems 29 (1) 69-82</dc:source>
<dc:subject>Group</dc:subject>
<dc:subject>neutral element</dc:subject>
<dc:subject>exponent</dc:subject>
<dc:subject>single axiom</dc:subject>
<dc:subject>automated reasoning</dc:subject>
<dc:title>Shortest single axioms with neutral element
for groups of exponent 2 and 3</dc:title>
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