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Simple groups of small Engel depth

Published online by Cambridge University Press:  17 April 2009

Rolf Brandl  and
Daniela B. Nikolova
Rolf Brandl
Affiliation:
Mathematisches Institut der Universität, Am Hubland 12, D-8700 Würzburg, BRD
Daniela B. Nikolova
Affiliation:
Mathematical Institute, Bulgarian Academy of Sciences, str. “Acad.G.Bonchev”, bl.8, 1113 Sofia, Bulgaria.
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Abstract

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It is proved that the simple group PSL (2,q) satisfies a law [x,3y] = [x, sy], s > 3, if and only if q = 4, 5, 8.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 2 , April 1986 , pp. 245 - 251
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Brandl, R., “On groups with small Engel depth”, Bull. Austral. Math. Soc. 28 (1983), 101–110.CrossRefGoogle Scholar
[2]Gupta, N. D., “Some group laws equivalent to the commutative law”, Arch. Math. (Basel) 17 (1966), 97–102.CrossRefGoogle Scholar
[3]Heineken, H. and Neumann, P.M., “Identical relations and decision procedures for groups”, J. Austral. Math. Soc. 7 (1967), 39–47.CrossRefGoogle Scholar
[4]Lang, S., Algebra, (Addison-Wesley, Reading, Massachusetts 1971).Google Scholar
[5]Nikolova, D. B., “Groups with a two-variable commutator identity”, R. Bulgare Sci. 36 (1983), 721–724.Google Scholar
[6]Schmidt, W. M., “A lower bound for the number of solutions of equations over finite fields”, J. Number Theory 6 (1974) 448–480.CrossRefGoogle Scholar