Palindromic width of finitely generated solvable groups. (English) Zbl 1344.20044

Bardakov, Valeriy G.; Gongopadhyay, Krishnendu

Commun. Algebra 43, No. 11, 4809-4824 (2015).

The authors investigate the palindromic width of finitely generated solvable groups. They show the finiteness of the palindromic width for finitely generated abelian-by-nilpotent-by-nilpotent groups (see Theorem 1.2). For arbitrary solvable groups, they prove the finiteness of the palindromic width, when the group \(G\) is solvable, finitely generated and possesses an abelian subgroup \(A\) such that quotient \(G/A\) satisfies the maximal condition on normal subgroups (see Theorem 1.1). In particular, finitely generated solvable groups of derived length \(\leq 3\) have finite palindromic width (see Corollary 1.3).

Reviewer: Francesco G. Russo (Rondebosch)

MSC:

20F16	Solvable groups, supersolvable groups
20F05	Generators, relations, and presentations of groups
20F19	Generalizations of solvable and nilpotent groups
20E22	Extensions, wreath products, and other compositions of groups

Keywords:

metabelian groups; palindromic widths; finitely generated solvable groups; commutator widths; commutators; products of palindromes

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