{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T06:43:29Z","timestamp":1774593809443,"version":"3.50.1"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2008,3]]},"abstract":"<jats:p>Let K be a field of any characteristic. We prove that a free metabelian Lie algebra M<jats:sub>3<\/jats:sub>of rank 3 over K admits wild automorphisms. Moreover, the subgroup I Aut M<jats:sub>3<\/jats:sub>of all automorphisms identical modulo the derived subalgebra [Formula: see text] cannot be generated by any finite set of IA-automorphisms together with the sets of all inner and all tame IA-automorphisms. In the case if K is finite the group Aut M<jats:sub>3<\/jats:sub>cannot be generated by any finite set of automorphisms together with the sets of all tame, all inner automorphisms and all one-row automorphisms. We present an infinite set of wild IA-automorphisms of M<jats:sub>3<\/jats:sub>which generates a free subgroup F<jats:sub>\u221e<\/jats:sub>modulo normal subgroup generated by all tame, all inner and all one-row automorphisms of M<jats:sub>3<\/jats:sub>.<\/jats:p>","DOI":"10.1142\/s0218196708004408","type":"journal-article","created":{"date-parts":[[2008,3,20]],"date-time":"2008-03-20T09:29:16Z","timestamp":1206005356000},"page":"209-226","source":"Crossref","is-referenced-by-count":10,"title":["ON THE AUTOMORPHISM GROUP OF A FREE METABELIAN LIE ALGEBRA"],"prefix":"10.1142","volume":"18","author":[{"given":"VITALY","family":"ROMAN'KOV","sequence":"first","affiliation":[{"name":"Department of Mathematics, Omsk State Dostoevskii University, Omsk, 644077, Russia"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"143","volume":"18","author":"Artamonov V. A.","journal-title":"Comment. Math. Univ. 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