TY - JOUR

T1 - Palindromic widths of nilpotent and wreath products

AU - Bardakov, Valeriy G.

AU - Bryukhanov, Oleg V.

AU - Gongopadhyay, Krishnendu

N1 - Publisher Copyright: © Indian Academy of Sciences.

PY - 2017/2

Y1 - 2017/2

N2 - We prove that the nilpotent product of a set of groups A1,..., As has finite palindromic width if and only if the palindromic widths of Ai, i = 1,..., s, are finite. We give a new proof that the commutator width of Fn ς K is infinite, where Fn is a free group of rank n ≥ 2 and K is a finite group. This result, combining with a result of Fink [9] gives examples of groups with infinite commutator width but finite palindromic width with respect to some generating set.

AB - We prove that the nilpotent product of a set of groups A1,..., As has finite palindromic width if and only if the palindromic widths of Ai, i = 1,..., s, are finite. We give a new proof that the commutator width of Fn ς K is infinite, where Fn is a free group of rank n ≥ 2 and K is a finite group. This result, combining with a result of Fink [9] gives examples of groups with infinite commutator width but finite palindromic width with respect to some generating set.

KW - Commutator width

KW - Nilpotent product

KW - Palindromic width

KW - Wreath products

KW - commutator width

KW - wreath products

KW - nilpotent product

UR - http://www.scopus.com/inward/record.url?scp=85012036980&partnerID=8YFLogxK

U2 - 10.1007/s12044-016-0296-1

DO - 10.1007/s12044-016-0296-1

M3 - Article

AN - SCOPUS:85012036980

VL - 127

SP - 99

EP - 108

JO - Proceedings of the Indian Academy of Sciences: Mathematical Sciences

JF - Proceedings of the Indian Academy of Sciences: Mathematical Sciences

SN - 0253-4142

IS - 1

ER -