<?xml version='1.0' encoding='utf-8'?>
<resource xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xmlns='http://datacite.org/schema/kernel-3' xsi:schemaLocation='http://datacite.org/schema/kernel-3 http://schema.datacite.org/meta/kernel-3/metadata.xsd'>
<creators>
<creator>
<creatorName>Fiala, N.</creatorName>
<affiliation>St. Cloud State University, Statele Unite ale Americii</affiliation>
</creator>
<creator>
<creatorName>Agre, K.M.</creatorName>
<affiliation>St. Cloud State University, Statele Unite ale Americii</affiliation>
</creator>
</creators>
<titles>
<title xml:lang='en'>Shortest single axioms with neutral element
for groups of exponent 2 and 3</title>
</titles>
<publisher>Instrumentul Bibliometric National</publisher>
<publicationYear>2013</publicationYear>
<relatedIdentifier relatedIdentifierType='ISSN' relationType='IsPartOf'>1561-2848</relatedIdentifier>
<subjects>
<subject>Group</subject>
<subject>neutral element</subject>
<subject>exponent</subject>
<subject>single axiom</subject>
<subject>automated reasoning</subject>
</subjects>
<dates>
<date dateType='Issued'>2013-02-01</date>
</dates>
<resourceType resourceTypeGeneral='Text'>Journal article</resourceType>
<descriptions>
<description xml:lang='en' descriptionType='Abstract'>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</description>
</descriptions>
<formats>
<format>application/pdf</format>
</formats>
</resource>