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Two-variable laws for PSL(2, 5)

To Bernhard Hermann Neumann on his 60th birthday

Published online by Cambridge University Press:  09 April 2009

R. M. Bryant  and
M. B. Powell
R. M. Bryant
Affiliation:
Mathematical Institute, Oxford
M. B. Powell
Affiliation:
Mathematical Institute and St. Peter's College, Oxford
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In [2], John Cossey and Sheila Oates Macdonald give a basis for the set of laws of PSL(2, 5) — the simple group of order 60 — and with one extreme exception the laws of their basis involve at most two variables. They raise the problem of finding a basis in which all of the laws involve only a small number of variables, and remark that they have shown that five variables will suffice. Here we give a basis consisting entirely of two variable laws.

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 10 , Issue 3-4 , November 1969 , pp. 499 - 502
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Bryant, R. M., D. Phil. thesis, to appear.Google Scholar
[2]John, Cossey and Sheila, Oates Macdonald, ‘A basis for the laws of PSL(2, 5)’, Bull. Amer. Math. Soc. 74 (1968), 602–606.Google Scholar
[3]Marshall, Hall Jr, ‘Solution of the Burnside problem for exponent six’, Illinois J. Math. 2 (1958), 764–786.Google Scholar
[4]Kovács, L. G. and Newman, M. F., ‘Cross varieties of groups’, Proc. Roy. Soc. Ser. A 292 (1966), 530–536.Google Scholar