Bulletin of the Belgian Mathematical Society - Simon Stevin

A property of group laws

Qianlu Li

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Abstract

For a word in $n$ letters, in [1] the author introduced a notion: \emph{its standard exponent} and proved that the variety of residually finite groups defined by a word is almost nilpotent if and only if the standard exponent of this word is 1. In this paper we obtain the following result: let $\omega(x_1, \cdots, x_n)$ denote a word in $x_1, \cdots, x_n$. Then both $\omega(x_1, \cdots, x_n)$ and $\omega(x^{m_1}_1, \cdots, x^{m_n}_n)$, where $m_i$ are natural numbers, have the same standard exponents.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 13, Number 3 (2006), 513-519.

Dates
First available in Project Euclid: 20 October 2006

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1161350692

Digital Object Identifier
doi:10.36045/bbms/1161350692

Mathematical Reviews number (MathSciNet)
MR2307686

Zentralblatt MATH identifier
1130.20033

Subjects
Primary: 20F10: Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70] 20E10: Quasivarieties and varieties of groups

Keywords
word standard exponent almost nilpotent

Citation

Li, Qianlu. A property of group laws. Bull. Belg. Math. Soc. Simon Stevin 13 (2006), no. 3, 513--519. doi:10.36045/bbms/1161350692. https://projecteuclid.org/euclid.bbms/1161350692


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