Abstract:
It is proved that in the braid group Bn for n⩾3 any proper verbal subgroup V(Bn) defined by a finite set of words V has infinite width relative to V. In addition, it is proved that in a colored braid group the taking of roots is unique and that the only element conjugate to its inverse is the identity.
\Bibitem{Bar92}
\by V.~G.~Bardakov
\paper On the theory of braid groups
\jour Russian Acad. Sci. Sb. Math.
\yr 1993
\vol 76
\issue 1
\pages 123--153
\mathnet{http://mi.mathnet.ru/eng/sm1044}
\crossref{https://doi.org/10.1070/SM1993v076n01ABEH003404}
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\zmath{https://zbmath.org/?q=an:0798.20029}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1993SbMat..76..123B}
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https://www.mathnet.ru/eng/sm1044
https://doi.org/10.1070/SM1993v076n01ABEH003404
https://www.mathnet.ru/eng/sm/v183/i6/p3
This publication is cited in the following 11 articles:
I. V. Dobrynina, D. Z. Kagan, “O shirine verbalnykh podgrupp v nekotorykh klassakh grupp”, Chebyshevskii sb., 16:4 (2015), 150–163
V. G. Bardakov, V. V. Vershinin, J. Wu, “On Cohen braids”, Proc. Steklov Inst. Math., 286 (2014), 16–32
V. G. Durnev, O. V. Zetkina, “Nekotorye rezultaty, poluchennye v Yaroslavskom otdelenii algebraicheskoi shkoly M. D. Grindlingera”, Chebyshevskii sb., 15:4 (2014), 5–31
Lee E.-K., Lee S.-J., “Uniqueness of Roots Up to Conjugacy for Some Affine and Finite Type Artin Groups”, Math. Z., 265:3 (2010), 571–587
Paolo Bellingeri, Sylvain Gervais, John Guaschi, “Lower central series of Artin–Tits and surface braid groups”, Journal of Algebra, 319:4 (2008), 1409
V. G. Bardakov, “Braid Groups in Genetic Code”, Algebra and Logic, 45:3 (2006), 75–91
V. N. Bezverkhnii, I. V. Dobrynina, “Normalizers of Some Classes of Subgroups in Braid Groups”, Math. Notes, 74:1 (2003), 18–29
V. G. Bardakov, “Structure of a Conjugating Automorphism Group”, Algebra and Logic, 42:5 (2003), 287–303
Faiziev V., Sahoo P., “Pseudocharacters and the Problem of Expressibility for Some Groups”, J. Algebra, 250:2 (2002), 603–637
V. N. Bezverkhnii, I. V. Dobrynina, “Reshenie problemy konechnoi shiriny v gruppakh Artina s dvumya obrazuyuschimi”, Chebyshevskii sb., 3:1 (2002), 11–16
Faiziev V., “A Problem of Expressibility in Some Amalgamated Products of Groups”, J. Aust. Math. Soc. A-Pure Math. Stat., 71:Part 1 (2001), 105–115
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