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The Groups of Steiner in Problems of Contact (Second Paper)
- Source :
- Transactions of the American Mathematical Society. 3:377
- Publication Year :
- 1902
- Publisher :
- JSTOR, 1902.
-
Abstract
- 1. Denote by G the group of the equation upon which depends the determi. nation of the curves of order n 3 having simple contact at 1 n ( n -3 ) points with a given curve C of order n having no double points. The case in which n is odd was discussed in the former paper (Transactions, January, 1902) and G was shown to be a subgroup of the group defined by the invariants 43, 04, , , * *, the latter group being holoedrically isomorphic with the first hypoabelian grouip on 2p indices with coefficients taken modulo 2. For n even, G is contained in the group H defined by the invariants 04' 069 * with even subscripts. JORDAN has shown (Traite, pp. 229-242) that H is holoedrically isomorphic with the abelian linear group A on 2p indices with coefficients taken modulo 2. The object of the present paper is to establish the latter theorem by a short, elementary proof, which makes no use of the abstract substitutions [al, 1 ., p, p1] of JORDAN, and which exhibits explicitly the correspondence t between the substitutions of the isomorphic groups.
Details
- ISSN :
- 00029947
- Volume :
- 3
- Database :
- OpenAIRE
- Journal :
- Transactions of the American Mathematical Society
- Accession number :
- edsair.doi...........74a4f112e68494f571ad3fc44636637c