Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-05T23:22:32.764Z Has data issue: false hasContentIssue false
  • English
  • Français

On the soluble length of groups with prime-power order

Published online by Cambridge University Press:  17 April 2009

Susan Evans-Riley ,
M.F. Newman  and
Csaba Schneider
Susan Evans-Riley
Affiliation:
School of Mathematics and Statistics, The University of Sydney, New South Wales 2006, Australia e-mail: [email protected]
M.F. Newman
Affiliation:
School of Mathematical Sciences, The Australian National University, Canberra ACT 0200, Australia e-mail: [email protected]
Csaba Schneider
Affiliation:
School of Mathematical Sciences, The Australian National University, Canberra ACT 0200, Australia e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that for every integer k ≥ 3 and every prime p ≤ 5 there is a group with soluble length k and order .

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 2 , April 1999 , pp. 343 - 346
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Blackburn, N., Problems on the theory of finite groups of prime-power order, (Ph.D. Thesis) (University of Cambridge, Cambridge, U.K., 1956).Google Scholar
[2]Blackburn, N., ‘On a special class of p-groups’, Acta Math. 100 (1958), 45–92.CrossRefGoogle Scholar
[3]Bosma, W., Cannon, J. and Playoust, C., ‘The Magma algebra system I: The user language’, J. Symbolic Comput. 24 (1997), 235–265.CrossRefGoogle Scholar
[4]Burnside, W., ‘On some properties of groups whose orders are powers of primes’, Proc. London Math. Soc. (2) 11 (1913), 225–243.CrossRefGoogle Scholar
[5]Burnside, W., ‘On some properties of groups whose orders are powers of primes’, (second paper), Proc. London Math. Soc. (2) 13 (1914), 6–12.CrossRefGoogle Scholar
[6]Caranti, A., Mattarei, S., Newman, M.F. and Scoppola, C.M., ‘Thin groups of prime-power order and thin Lie algebras’, Quart. J. Math. Oxford (2) 47 (1996), 279–296.CrossRefGoogle Scholar
[7]Gruenberg, K.W. and Roseblade, J.E. (eds), The collected works of Philip Hall (Clarendon Press, Oxford, 1988).Google Scholar
[8]Hall, P., ‘A contribution to the theory of groups of prime-power order’, Proc. London Math. Soc. (2) 36 (1934), 29–95; or collected works [7] pp. 57–125.CrossRefGoogle Scholar
[9]Hall, P., ‘A note on -groups’, J. London Math. Soc. 39 (1964), 338–344; or collected works [7] pp. 653–661.CrossRefGoogle Scholar
[10]Havas, G., Newman, M.F. and O'Brien, E.A., ‘The ANU p-Quotient Program (version 1.4)’, The Australian National University, Canberra, (1996); Available as part of GAP [15] and MAGMA [3]; also via ftp from ftpmaths.anu.edu.au/pub/algebra/PQ/.Google Scholar
[11]Huppert, B., Endliche Gruppen I, Die Grundlehren der Mathematischen Wissenschaften 134 (Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
[12]Itô, N., ‘Note on p-groups’, Nagoya Math. J. 1 (1950), 113–116.CrossRefGoogle Scholar
[13]Klaas, G., Leedham-Green, C.R. and Plesken, W., Linear pro-p-groups of finite width, Lecture Notes in Mathematics 1674 (Springer-Verlag, Berlin, Heidelberg, New York, 1997).CrossRefGoogle Scholar
[14]Nickel, W., ‘The ANU Nilpotent Quotient Program (version 1.2)’, Available as part of GAP [15]; also via ftp from ftpmaths.anu.edu.au/pub/algebra/NQ/.Google Scholar
[15]Schönert, M. et al. , GAP – Groups, Algorithms and Programming, (fifth edition) (Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany, 1995).Google Scholar