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A basis for the laws of a class of simple groups

Published online by Cambridge University Press:  09 April 2009

Bruce Southcott
Bruce Southcott
Affiliation:
Department of Mathematics, University of Queensland, St. Lucia, Queensland, Australia
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This paper presents a basis for the laws which hold in each of the finite simple groups, PSL(2, 2n), n> ≥ 2, thus partially solving a problem raised by Cossey, Macdonald and Street [3]. They considered the more general problem of finding bases for the laws which hold in PSL(2, pn), and succeded in finding a number of general laws, and in completing bases for pn ≤ 11. The solution of the general problem appears to be very difficult.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 4 , June 1974 , pp. 500 - 505
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Bryant, Roger M., ‘On the laws of certain linear groups’, J. London Math. Soc. (2), 4 (1971), 309–313.CrossRefGoogle Scholar
[2]Bryant, R. M. and Powell, M. B., ‘Two variable laws for PSL (2, 5)’, J. Austral. Math. Soc. 10 (1969), 499–502.CrossRefGoogle Scholar
[3]Cossey, John, Macdonald, Sheila Oates and Street, Anne Penfold, ‘On the laws of certain finite groups’, J. Austral. Math. Soc. 11 (1970), 441–489.CrossRefGoogle Scholar
[4]Kovács, L. G. and Newman, M. F., ‘On critical groups’, J. Austral. Math. Soc. 6 (1966). 237–250.CrossRefGoogle Scholar