Hostname: page-component-f554764f5-rj9fg Total loading time: 0 Render date: 2025-04-12T22:13:40.670Z Has data issue: false hasContentIssue false
  • English
  • Français

A computer aided classification of certain groups of prime power order

Published online by Cambridge University Press:  17 April 2009

Judith A. Ascione ,
George Havas  and
C. R. Leedham-Green
Judith A. Ascione
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT;
George Havas
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT;
C. R. Leedham-Green
Affiliation:
Department of Pure Mathematics, Queen Mary College, University of London, London, England.
Rights & Permissions [Opens in a new window]

Extract

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.

A classification of two-generator 3-groups of second maximal class and low order is presented. All such groups with orders up to 38 are described, and in some cases with orders up to 310. The classification is based on computer aided computations. A description of the computations and their results are presented, together with an indication of their significance.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 17 , Issue 2 , October 1977 , pp. 257 - 274
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Alperin, J.L., “Automorphisms of solvable groups”, Proc. Amer. Math. Soc. 13 (1962), 175–180.CrossRefGoogle Scholar
[2]Blackburn, N., “On a special class of p-groups”, Acta Math. 100 (1958), 45–92.Google Scholar
[3]Conlon, S.B., “Three-groups with cyclic centre and central quotient of maximal class”, J. Austral. Math. Soc. Ser. A (to appear).Google Scholar
[4]James, Rodney, “2-groups of almost maximal class”, J. Austral. Math. Soc. Ser. A 19 (1975), 343–357.CrossRefGoogle Scholar
[5]Leedham-Green, C.R., “Three-groups of second maximal class”, in preparation.Google Scholar
[6]Leedham-Green, C.R., “On p-groups of large class”, in preparation.Google Scholar
[7]Newman, M.F., “Calculating presentations for certain kinds of quotient groups”, SYMSAC ′76, 2–8 (Proc. ACM Sympos. Symbolic and Algebraic Computation,New York,1976.Association for Computing Machinery, New York, 1976).CrossRefGoogle Scholar
[8]Newman, M.F., “Determination of groups of prime-power order”, Group Theory, Canberra 1975, 73–84 (Proc. Miniconf. Australian National University,1975.Lecture Notes in Mathematics, 573. Springer-Verlag,Berlin, Heidelberg, New York, 1977).CrossRefGoogle Scholar
[9]Shepherd, Raymond T., “p-groups of maximal class” (PhD thesis, University of Chicago, Chicago, Illinois, 1970).Google Scholar