{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,15]],"date-time":"2024-02-15T13:23:10Z","timestamp":1708003390501},"reference-count":8,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>We give a set of axioms to establish a perpendicularity relation in an Abelian group and then study the existence of perpendicularities in<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:msub><mml:mi>\u2124<\/mml:mi><mml:mi>n<\/mml:mi><\/mml:msub><mml:mo>,<\/mml:mo><mml:mo>+<\/mml:mo><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:msub><mml:mi>\u211a<\/mml:mi><mml:mo>+<\/mml:mo><\/mml:msub><mml:mo>,<\/mml:mo><mml:mo>\u00b7<\/mml:mo><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:math>and in certain other groups. Our approach provides a justification for the use of the symbol<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mo>\u22a5<\/mml:mo><\/mml:mrow><\/mml:math>denoting relative primeness in number theory and extends the domain of this convention to some degree. Related to that, we also consider parallelism from an axiomatic perspective.<\/jats:p>","DOI":"10.1155\/2013\/983607","type":"journal-article","created":{"date-parts":[[2013,4,29]],"date-time":"2013-04-29T21:03:35Z","timestamp":1367269415000},"page":"1-8","source":"Crossref","is-referenced-by-count":2,"title":["Perpendicularity in an Abelian Group"],"prefix":"10.1155","volume":"2013","author":[{"given":"Pentti","family":"Haukkanen","sequence":"first","affiliation":[{"name":"School of Information Sciences, University of Tampere, 33014, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mika","family":"Mattila","sequence":"additional","affiliation":[{"name":"School of Information Sciences, University of Tampere, 33014, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jorma K.","family":"Merikoski","sequence":"additional","affiliation":[{"name":"School of Information Sciences, University of Tampere, 33014, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Timo","family":"Tossavainen","sequence":"additional","affiliation":[{"name":"School of Applied Educational Science and Teacher Education, University of Eastern Finland, P.O. 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