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Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 1, Pages 89–94 (Mi izv2212)  

On the orders of free groups of locally finite varieties

A. Yu. Ol'shanskii


Abstract: The results of [4] are used here to show that there exists a continuum of locally finite varieties of groups with pairwise distinct “ordinal” functions, thus disproving a conjecture of G. Higman. On the other hand, an example is given of distinct varieties having the same “ordinal” function.

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:1, 85–90

Bibliographic databases:

UDC: 519.4
MSC: 20E05, 20E10, 20E25
Received: 29.11.1971

Citation: A. Yu. Ol'shanskii, “On the orders of free groups of locally finite varieties”, Izv. Akad. Nauk SSSR Ser. Mat., 37:1 (1973), 89–94; Math. USSR-Izv., 7:1 (1973), 85–90

Citation in format AMSBIB
\Bibitem{Ols73}
\by A.~Yu.~Ol'shanskii
\paper On the orders of free groups of locally finite varieties
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 1
\pages 89--94
\mathnet{http://mi.mathnet.ru/izv2212}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=354868}
\zmath{https://zbmath.org/?q=an:0254.20016}
\transl
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 1
\pages 85--90
\crossref{https://doi.org/10.1070/IM1973v007n01ABEH001926}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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