{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,7]],"date-time":"2023-02-07T05:21:41Z","timestamp":1675747301113},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"name":"Ministry for Innovation and Technology, Hungary","award":["NKFIH-1279-2\/2020","TKP2021-NVA-09","NKFIH-K128042","NKFIH-K138892"],"award-info":[{"award-number":["NKFIH-1279-2\/2020","TKP2021-NVA-09","NKFIH-K128042","NKFIH-K138892"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2023,2]]},"abstract":"<jats:p> We have recently published a result that [Formula: see text]-permutability is not join-prime in the lattice of interpretability types of varieties whenever [Formula: see text]. In the proof, we showed that if [Formula: see text], then the join of a properly chosen finitely generated non-[Formula: see text]-permutable variety and the variety [Formula: see text] defined by the majority identities is [Formula: see text]-permutable. In the present note, we prove that the join of any locally finite non-3-permutable variety with [Formula: see text] is non-3-permutable. We also prove that the join of any non-2-permutable variety with [Formula: see text] is non-2-permutable. Our non-3-permutable result gives that one has to use a nonlocally finite non-3-permutable variety [Formula: see text] if they want to prove that 3-permutability is not join-prime by arguing that [Formula: see text] is 3-permutable. <\/jats:p>","DOI":"10.1142\/s0218196723500042","type":"journal-article","created":{"date-parts":[[2022,11,22]],"date-time":"2022-11-22T09:30:55Z","timestamp":1669109455000},"page":"31-46","source":"Crossref","is-referenced-by-count":0,"title":["On the use of majority for investigating primeness of 3-permutability"],"prefix":"10.1142","volume":"33","author":[{"given":"Gerg\u0151","family":"Gyenizse","sequence":"first","affiliation":[{"name":"Bolyai Institute, University of Szeged, Szeged 6720, Hungary"}]},{"given":"Mikl\u00f3s","family":"Mar\u00f3ti","sequence":"additional","affiliation":[{"name":"Bolyai Institute, University of Szeged, Szeged 6720, Hungary"}]},{"given":"L\u00e1szl\u00f3","family":"Z\u00e1dori","sequence":"additional","affiliation":[{"name":"Bolyai Institute, University of Szeged, Szeged 6720, Hungary"},{"name":"R\u00e9nyi Institute, Budapest 1053, Hungary"}]}],"member":"219","published-online":{"date-parts":[[2022,11,21]]},"reference":[{"key":"S0218196723500042BIB001","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1007\/s00012-019-0594-4","volume":"80","author":"Chicco A.","year":"2019","journal-title":"Algebra Universalis"},{"key":"S0218196723500042BIB002","first-page":"v+125","volume":"50","author":"Garcia O. 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