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On the laws of certain finite groups

Published online by Cambridge University Press:  09 April 2009

John Cossey ,
Sheila Oates MacDonald  and
Anne Penfold Street
John Cossey
Affiliation:
Department of Pure MathematicsSchool of General StudiesAustralian National UniversityCanberra
Sheila Oates MacDonald
Affiliation:
Department of MathematicsUniversity of QueenslandBrisbane
Anne Penfold Street
Affiliation:
Department of MathematicsUniversity of QueenslandBrisbane
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In recent years a great deal of attention has been devoted to the study of finite simple groups, but one aspect which seems to have been little considered is that of the laws they satisfy. In a recent paper [3], the first two of the present authors gave a basis for laws of PSL(2, 5). The techniques of [3] can be used to show that (modulo certain classification problems) a basis for the laws of PSL(2, pn) can be made up from laws of the following types:

(1) an exponent law,

(2) laws which determine the Sylow subgroups,

(3) laws which determine the normalisers of the Sylow subgroups,

(4) in certain special cases, laws which determine subvarieties of smaller exponent, e.g. the subvariety of exponent 12 for those PSL(2, pn) which contain S4,

(5) a law implying local finiteness.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 4 , November 1970 , pp. 441 - 489
Copyright
Copyright © Australian Mathematical Society 1970

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