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Soluble linear groups

Published online by Cambridge University Press:  17 April 2009

M. Frick  and
M.F. Newman
M. Frick
Affiliation:
Department of Pure Mathematics, School of General Studies, Australian National University, Canberra, ACT
M.F. Newman
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Abstract

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The least upper bound for the nilpotent lengths of soluble linear groups of degree n is calculated. For each n it is , where r(n) = [log3 (2n–1)/4] and [x] is the integral part of x.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 6 , Issue 1 , February 1972 , pp. 31 - 44
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Dixon, John D., “The solvable length of a solvable linear group”, Math. Z. 107 (1968), 151–158.CrossRefGoogle Scholar
[2]Huppert, B., Endliche Gruppen I (Die Grundlehren der mathematischen Wissenschaften, Band 134. Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
[3]Makan, A.R., “On some aspects of finite soluble groups”, (Ph.D. thesis, Australian National University, Canberra, 1971).Google Scholar
[4]Mal'cev, A.I., “On certain classes of infinite solvable groups”, Amer. Math. Soc. Transl. (2) 2 (1956), 1–21.Google Scholar
[5]Newman, M.F., “The soluble length of soluble linear groups”, Submitted to Math. Z.Google Scholar
[6]Suprunenko, D. [A.], Soluble and nilpotent linear groups (Transl. Math. Monographs, 9. Amer. Math. Soc., Providence, Rhode Island, 1963).Google Scholar