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 Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 6, Pages 1308–1325 (Mi izv1575)

A new identity in the Lie ring of a free group of prime exponent, and groups without the Hughes property

E. I. Khukhro

Abstract: A multilinear identity of degree $3p-2$ is given in explicit form, and it is shown that this identity holds in the associated Lie ring of a free group of prime exponent $p$. It is also shown that if this identity is not a consequence of the known identities of Wall of degree $2p-1$ and the $(p-1)$st Engel identity, there exists a finite $p$-group in which the index of the (nontrivial) Hughes subgroup is $p^3$.
Bibliography: 13 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1987, 29:3, 659–676

Bibliographic databases:

UDC: 519.4
MSC: Primary 20F40; Secondary 20D15

Citation: E. I. Khukhro, “A new identity in the Lie ring of a free group of prime exponent, and groups without the Hughes property”, Izv. Akad. Nauk SSSR Ser. Mat., 50:6 (1986), 1308–1325; Math. USSR-Izv., 29:3 (1987), 659–676

Citation in format AMSBIB
\Bibitem{Khu86} \by E.~I.~Khukhro \paper A~new identity in the Lie ring of a~free group of prime exponent, and groups without the Hughes property \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1986 \vol 50 \issue 6 \pages 1308--1325 \mathnet{http://mi.mathnet.ru/izv1575} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=883163} \zmath{https://zbmath.org/?q=an:0633.20027|0619.20016} \transl \jour Math. USSR-Izv. \yr 1987 \vol 29 \issue 3 \pages 659--676 \crossref{https://doi.org/10.1070/IM1987v029n03ABEH000987}