Geodesic
A~new identity in the Lie ring of a~free group of prime exponent, and groups without the Hughes property
Izvestiya. Mathematics , Tome 29 (1987) no. 3, pp. 659-676

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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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     author = {E. I. Khukhro},
     title = {A~new identity in the {Lie} ring of a~free group of prime exponent, and groups without the {Hughes} property},
     journal = {Izvestiya. Mathematics },
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E. I. Khukhro. A~new identity in the Lie ring of a~free group of prime exponent, and groups without the Hughes property. Izvestiya. Mathematics , Tome 29 (1987) no. 3, pp. 659-676. http://geodesic.mathdoc.fr/item/IM2_1987_29_3_a7/