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A new determination of the primitive continuous groups in two variables
- Source :
- Transactions of the American Mathematical Society. 2:249-258
- Publication Year :
- 1901
- Publisher :
- American Mathematical Society (AMS), 1901.
-
Abstract
- The primitive continuous groups of point-transformations in two variables can, by a proper choice of the variables, be transformed into projective groups of the plane, a result LIE obtains after determining the canonical forms of the primitive groups.t This fact canl, however, be established from the general properties of such groups, and its use leads to a new determination of these primitive groups, to show which is the object of this paper. A primitive group will be defined as a group which does not leave invariant a differential equiation of the first ordert Such a group is at least three-parametric, as a two-parametric group possesses a differential invariant of the first order, J say, and therefore an invariant differential equation of the first order, f(J) = constant.?
Details
- ISSN :
- 10886850 and 00029947
- Volume :
- 2
- Database :
- OpenAIRE
- Journal :
- Transactions of the American Mathematical Society
- Accession number :
- edsair.doi...........367d40f97daabaa91da2b2dfe716608d