Access the full text.
Sign up today, get DeepDyve free for 14 days.
L E Dickson (1901)
Linear groups
G. Miller (1920)
Groups Generated by Two Operators of Order Three Whose Product Is of Order Six.Proceedings of the National Academy of Sciences of the United States of America, 13 3
J. Singer (1938)
A theorem in finite projective geometry and some applications to number theoryTransactions of the American Mathematical Society, 43
Jr. Hall (1947)
Cyclic projective planesDuke Mathematical Journal, 14
O. Veblen, W. Bussey (1906)
Finite projective geometriesTransactions of the American Mathematical Society, 7
A Hurwitz (1896)
Über die Zahlentheorie der QuaternionenMathematische Werke, 2
H. Blichfeldt (1905)
The finite, discontinuous, primitive groups of collineations in three variablesMathematische Annalen, 63
G. Miller, H. Blichfeldt, L. Dickson
Theory and applications of finite groups
H. Brahana (1930)
Pairs of Generators of the Known Simple Groups whose Orders are Less than One MillionAnnals of Mathematics, 31
G A Miller (1920)
Groups generated by two operators of order three whose product is of order fourBull. Amer. Math. Soc., 26
J. Todd, H. Coxeter (1936)
A practical method for enumerating cosets of a finite abstract group, 5
W. Threlfall, H. Seifert (1931)
Topologische Untersuchung der Diskontinuitätsbereiche endlicher Bewegungsgruppen des dreidimensionalen sphärischen Raumes (Schluß)Mathematische Annalen, 107
H. Coxeter (1940)
The binary polyhedral groups, and other generalizations of the quaternion groupDuke Mathematical Journal, 7
L. Hua, I. Reiner (1949)
On the generators of the symplectic modular groupTransactions of the American Mathematical Society, 65
The collineation groups oE the finite affine and projective planes with four lines through each point Dedicated to WILHELM BLASCHKE on his seventieth birthday By H. S. M. COXETER in Toronto The group of all collineations in the finite projective plane PG(2, 3) is the simple group LF(3, 3) of order 5616. BRAHANA (1930, p.531) gave two matrices which generate this group, but did not attempt to find a complete set of defining relations. In terms of a different pair of generators, such relations are now found to be (1) 8 = T3 = (8T)4 = (S2T)4 = (8 T)3 = E, 2 2 2 2 (T8 T)28 = 8 (T8 T)2. These are established by enumerating the 26 cosets of the subgroup T3 = U3 = (TU)4 = E, (TUT)2U = U(TUT)2 (2) (where U = 8 ), which is the Hessian group of order 216, i. e., the group of projective collineations leaving invariant the nine inflexions of the general cubic curve in the complex projective plane. This, in turn, has a 8ubgroup of index 9: (3) U3 = E, U V U = V U V (where V = T-l U T), which is the binary
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals
Published: Aug 1, 1956
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.