Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-23T02:57:59.205Z Has data issue: false hasContentIssue false
  • English
  • Français

The two generator restricted Burnside group of exponent five

Published online by Cambridge University Press:  17 April 2009

George Havas ,
G.E. Wall  and
J.W. Wamsley
George Havas
Affiliation:
School of Information Sciences, Canberra College of Advanced Education, Canberra
G.E. Wall
Affiliation:
Department of Pure Mathematics, University of Sydney, Sydney, New South Wales
J.W. Wamsley
Affiliation:
School of Mathematical Sciences, Flinders University of South Australia, Bedford Park, South Australia.
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.

The two generator restricted Burnside group of exponent five is shown to have order 534 and class 12 by two independent methods. A consistent commutator power presentation for the group is given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 10 , Issue 3 , June 1974 , pp. 459 - 470
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Adyan, S.I., “Periodic groups of odd exponent”, Proc. Second Internat. Conf. Theory of Groups, Canberra, 1973 (Lecture Notes in Mathematics. Springer-Verlag, Berlin, Heidelberg, New York, to appear).Google Scholar
[2]Alford, William A., Havas, George and Newman, M.F., “Groups of exponent 4”, Notices Amer. Math. Soc. 21 (1974), A–291.Google Scholar
[3]Bayes, A.J., Kautsky, J. and Wamsley, J.W., “Computation in nilpotent groups (application)”, Proc. Second Internat. Conf. Theory of Groups, Canberra, 1973 (Lecture Notes in Mathematics. Springer-Verlag, Berlin, Heidelberg, New York, to appear).Google Scholar
[4]Burnside, W., “On an unsettled question in the theory of discontinuous groups”, Quart. J. Pure Appl. Math. 33 (1902), 230–238.Google Scholar
[5]Havas, George, “Computational approaches to combinatorial group theory”, PhD thesis, University of Sydney, 02, 1974.Google Scholar
[6]Кострикин, A.И. [A.I. Kostrikin], “Решение ослабленой проблемы Бернсайда для показателя 5” [Solution of a weakened problem of Burnside for exponent 5”, Izv. Akad. Nauk SSSR Ser. Mat. 19 (1955), 233–244; MR17,126.Google Scholar
[7]Кострикин, A.И. [A.I. Kostrikin], “О связи между периодическими группами и кольцами Ли” [On the connection between periodic groups and Lie rings”, Izv. Akad. Nauk SSSR Ser. Mat. 21 (1957), 289–310; Amer. Math. Soc. Transl. (2) 45 (1965), 165–189.Google ScholarPubMed
[8]Кострикин, A.И. [A.I. Kostrikin], “О проблеме Бернсайда” [The Burnside problem], Izv. Akad. Nauk SSSR Ser. Mat. 23 (1959), 3–34; Amer. Math. Soc. Transl. (2) 36 (1964), 63–99.Google Scholar
[9]Krause, Eugene F. and Weston, Kenneth W., “On the Lie algebra of a Burnside group of exponent 5”, Proc. Amer. Math. Soc. 27 (1971), 463–470.CrossRefGoogle Scholar
[10]Macdonald, I.D., “A computer application to finite p–groups”, J. Austral. Math. Soc. 17 (1974), 102–112.CrossRefGoogle Scholar
[11]Новиков, П.С., Адян, С.И. [P.S. Novikov, S.I. Adyan], “О бесконечных периодических группах. I” [Infinite periodic groups. I], Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 212–244; Math. USSR-Izv. 2 (1968), 209–236 (1969).Google Scholar
[12]Новиков, П.С., Адян, С.И. [P.S. Novikov, S.I. Adyan], “О бесконечных периодических группах. II” [Infinite periodic groups. II], Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 251–524; Math. USSR-Izv. 2 (1968), 241–479 (1969).Google ScholarPubMed
[13]Новиков, П.С., Адян, С.И. [P.S. Novikov, S.I. Adyan], “О бесконечных периодических группах. III” [Infinite periodic groups. III], Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 709–731; Math. USSR-Izv. 2 (1968), 665–685 (1969).Google Scholar
[14]Санов, И.Н. [I.N. Sanov], “Установление связи между периодическими пруппами с периодом простым числом и кольцами Ли” [Establishment of a connection between periodic groups with period a prime number and Lie rings], Izv. Akad. Nauk SSSR Ser. Mat. 16 (1952), 23–58.Google ScholarPubMed
[15]Wall, G.E., “On Hughes' Hp problem”, Proc. Internat. Conf. Theory of Groups, Canberra, 1965, 357–362 (Gordon and Breach, New York, 1967).Google Scholar
[16]Wall, G.E., “On the Lie ring of a group of prime exponent”, Proc. Second Internat. Conf. Theory of Groups, Canberra, 1973 (Lecture Notes in Mathematics. Springer-Verlag, Berlin, Heidelberg, New York, to appear).Google Scholar
[17]Wamsley, J.W., “Computation in nilpotent groups (theory)”, Proc. Second Internat. Conf. Theory of Groups, Canberra, 1973 (Lecture Notes in Mathematics. Springer-Verlag, Berlin, Heidelberg, New York, to appear).Google Scholar