On solvable Lie algebras with one defining relation

DOI10.1007/BF00967768zbMath0477.17005MaRDI QIDQ1160739

V. V. Talapov

Publication date: 1981

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

solvabilityword problemalgorithmic problemsfree subalgebraLie algebras with single relationmethod of Lie wreath productsvariety of k-solvable algebras

Mathematics Subject Classification ID

Infinite-dimensional Lie (super)algebras (17B65) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Solvable, nilpotent (super)algebras (17B30) Word problems, etc. in computability and recursion theory (03D40) Lie algebras and Lie superalgebras (17B99) Word problems (aspects of algebraic structures) (08A50)

Related Items (4)

Relative linear dependence problem for the variety \({\mathfrak AN}_ {\mathbf{c}}\) of Lie algebras ⋮ Primitive and almost primitive elements of Schreier varieties ⋮ Polynilpotent Lie algebras given by one defining relation ⋮ A Lie algebra with a single defining relation need not be residually finite

Cites Work

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• A solvable group admitting a regular splitting automorphism of prime order is nilpotent
• A FREEDOM THEOREM FOR GROUPS WITH ONE DEFINING RELATION IN THE VARIETIES OF SOLVABLE AND NILPOTENT GROUPS OF GIVEN LENGTHS

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