Geodesic
Infinite periodic words and almost nilpotent varieties
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2017), pp. 62-66 Cet article a éte moissonné depuis la source Math-Net.Ru

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An almost nilpotent variety of linear growth is constructed in the paper for any infinite periodic word in an alphabet of two letters. A discrete series of different almost nilpotent varieties is also constructed. Only a few almost nilpotent varieties were studied previously and their existence was proved often under some additional assumptions. It was proved the existence of almost nilpotent varieties of any integer exponent with a fractional exponent, as well as the existence of a continual family of almost nilpotent varieties with not more than quadratic growth. 
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     title = {Infinite periodic words and almost nilpotent varieties},
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S. P. Mishchenko. Infinite periodic words and almost nilpotent varieties. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2017), pp. 62-66. http://geodesic.mathdoc.fr/item/VMUMM_2017_4_a10/

[1] Giambruno A., Zaicev M., Polynomial identities and asymptotic methods, Math. Surveys and Monographs, 122, Amer. Math. Soc., Providence, RI, 2005 | DOI | MR | Zbl

[2] Frolova Yu.Yu., Shulezhko O.V., “Pochti nilpotentnye mnogoobraziya algebr Leibnitsa”, Prikladnaya diskretnaya matematika. Tomsk, 2015, no. 2(28), 30–36

[3] Mishchenko S., Valenti A., “On almost nilpotent varieties of subexponential growth”, J. Algebra, 423:1 (2015), 902–915 | DOI | MR | Zbl

[4] Mishchenko S., Valenti A., “An almost nilpotent variety of exponent 2”, Isr. J. Math., 199 (2014), 241–258 | DOI | MR

[5] Shulezhko O.V., “Novye svoistva pochti nilpotentnogo mnogoobraziya eksponenty dva”, Izv. Saratov. un-ta. Novaya ser. Matem. Mekhan. Inform., 14:3 (2014), 316–320 | Zbl

[6] Mischenko S.P., Shulezhko O.V., “Pochti nilpotentnye mnogoobraziya lyuboi tseloi eksponenty”, Vestn. Mosk. un-ta. Matem. Mekhan., 2015, no. 2, 53–57

[7] Mischenko S.P., “Pochti nilpotentnye mnogoobraziya drobnoi eksponenty suschestvuyut”, Vestn. Mosk. un-ta. Matem. Mekhan., 2016, no. 3, 42–46

[8] Mischenko S.P., “Metabelevy pochti nilpotentnye mnogoobraziya polinomialnogo rosta”, Mat-ly Mezhdunar. konf. po algebre, analizu i geometrii, Kazan. un-t, Kazan; Izd-vo Akademii nauk TR, 2016, 247–248

[9] Shulezhko O.V., “O pochti nilpotentnykh mnogoobraziyakh v razlichnykh klassakh lineinykh algebr”, Chebyshevskii sbornik, 16:1 (2015), 67–88 | MR

[10] Mischenko S.P., Verevkin A.B., “O mnogoobraziyakh s tozhdestvami odnoporozhdennoi svobodnoi metabelevoi algebry”, Chebyshevskii sbornik, 17:2(58) (2016), 21–55 | MR

[11] Zaitsev M.V., Mischenko S.P., “O kodline mnogoobrazii lineinykh algebr”, Matem. zametki, 79:4 (2006), 553–559 | DOI | Zbl