{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T07:32:33Z","timestamp":1648971153438},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2015,5]]},"abstract":"<jats:p> Let \u212c<jats:sub>n<\/jats:sub> be the variety of groups satisfying the identity x<jats:sup>n<\/jats:sup> = 1. It is proved that for every sufficiently large prime p, say p &gt; 10<jats:sup>10<\/jats:sup>, the product \u212c<jats:sub>p<\/jats:sub>\u212c<jats:sub>p<\/jats:sub> cannot be defined by a finite set of identities. This solves the problem formulated by C. K. Gupta and A. N. Krasilnikov in 2003. We also find the axiomatic and the basis ranks of the variety \u212c<jats:sub>p<\/jats:sub>\u212c<jats:sub>p<\/jats:sub>. For this goal, we improve the estimate for the basis rank of the product of group varieties obtained by G. Baumslag, B. H. Neumann, H. Neumann and P. M. Neumann in 1964. <\/jats:p>","DOI":"10.1142\/s0218196715500083","type":"journal-article","created":{"date-parts":[[2015,2,25]],"date-time":"2015-02-25T10:11:16Z","timestamp":1424859076000},"page":"531-540","source":"Crossref","is-referenced-by-count":1,"title":["On identities in the products of group varieties"],"prefix":"10.1142","volume":"25","author":[{"given":"Nicholas S.","family":"Boatman","sequence":"first","affiliation":[{"name":"Vanderbilt University, USA"}]},{"given":"Alexander","family":"Yu Olshanskii","sequence":"additional","affiliation":[{"name":"Vanderbilt University, Nashville 37240, USA"},{"name":"Moscow State University, Moscow 119991, Russia"}]}],"member":"219","published-online":{"date-parts":[[2015,4,9]]},"reference":[{"key":"rf1","first-page":"721","volume":"34","author":"Adyan S. 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