Geodesic
Engel Congruences in Groups of Prime-Power Exponent
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1321-1323

Voir la notice de l'article provenant de la source Cambridge University Press

It is a well-known result of Sanov (5) that groups of exponent pk (p prime) satisfy the th Engel congruence (definition below). Recently, an alternative proof of this has been given by Glauberman, Krause, and Struik (3). Bruck (2) has conjectured that such groups satisfy the th Engel congruence. In this note we go some way towards proving this. 
Gupta, N. D.; Newman, M. F. Engel Congruences in Groups of Prime-Power Exponent. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1321-1323. doi: 10.4153/CJM-1968-131-5
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[1] 1. Bachmuth, S. and Mochizuki, H. Y., Cyclotomic ideals in group rings, Bull. Amer. Math. Soc. 72 (1966), 1018–1020. Google Scholar

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[3] 3. Glauberman, George, Krause, Eugene F., and Rebekka Struik, Ruth, Engel congruences in groups of prime-power exponent, Can. J. Math. 18 (1966), 579–588. Google Scholar

[4] 4. Gupta, N. D., Newman, M. F., and Tobin, S. J., On metabelian groups of prime-power exponent, Proc. Roy. Soc. London Ser. A 802 (1968), 237–242. Google Scholar

[5] 5. Sanov, I. N., On a certain system of relations in periodic groups with period a power of a prime number, Izv. Akad. Nauk SSSR Ser. Mat. 15 (1951), 477–502. Google Scholar

[6] 6. Tobin, Seán, On a theorem of Baer and Higman, Can. J. Math. 8 (1956), 263–270. Google Scholar

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